This notebook contains all multivariate analyses of zoobenthic community structure using the new, nearly unheard-of modeling methods: packages mvabund, boral.
Again, to make it self-contained, there will be the same repetitive setup/data import/preparation part.


Setup!

Define the working subdirectories.

## print the working directory, just to be on the safe side
paste("You are here: ", getwd())

data.dir <- "data"    ## input data files
functions.dir <- "R"  ## functions & scripts
save.dir <- "output"  ## clean data, output from models & more complex calculations
figures.dir <- "figs" ## plots & figures 

Import libraries.

library(here) ## painless relative paths to subdurectories, etc.
library(tidyverse) ## data manipulation, cleaning, aggregation
library(viridis) ## smart & pretty colour schemes
library(mvabund) ## multivariate modeling analyses in ecology
library(boral) ## more multivariate modeling analyses in ecology

Organize some commonly-used ggplot2 modifications into a more convenient (and less repetitive) format. One day, I MUST figure out the proper way to set the theme..

## ggplot settings & things that I keep reusing
# ggplot_theme <- list(
#   theme_bw(),
#   theme(element_text(family = "Times"))
# )
## always use black-and-white theme
theme_set(theme_bw())
## helper to adjust ggplot text size & avoid repetitions 
text_size <- function(text.x = NULL,
                      text.y = NULL,
                      title.x = NULL,
                      title.y = NULL,
                      legend.text = NULL,
                      legend.title = NULL, 
                      strip.x = NULL, 
                      strip.y = NULL) {
  theme(axis.text.x = element_text(size = text.x),
        axis.text.y = element_text(size = text.y),
        axis.title.x = element_text(size = title.x),
        axis.title.y = element_text(size = title.y),
        legend.text = element_text(size = legend.text), 
        legend.title = element_text(size = legend.title), 
        strip.text.x = element_text(size = strip.x), 
        strip.text.y = element_text(size = strip.y)
        )
}
## log y/min + 1 transform - useful for species counts/biomass data visualization
log_y_min <- function(y) {
  log(y / min(y[y > 0]) + 1)
}

Sand stations (Burgas Bay, 2013-2014)

Import zoobenthic abundance data (cleaned and prepared).

zoo.abnd.sand <- read_csv(here(save.dir, "abnd_sand_orig_clean.csv"))

## convert station to factor (better safe than sorry later, when the stations are not plotted in the order I want them)
(zoo.abnd.sand <- zoo.abnd.sand %>% 
    mutate(station = factor(station, levels = c("Kraimorie", "Chukalya", "Akin", "Sozopol", "Agalina", "Paraskeva")))
)

Remove the all-0 species (= not present in the current dataset).
Maybe also remove the singletons (species appearing only once in the whole dataset and represented by a single individual = so rare that it’s unlikely they carry important information, but it would probably improve the run times).

(zoo.abnd.flt.sand <- zoo.abnd.sand %>%
   select(-c(station:replicate)) %>%
   select(which(colSums(.) > 0))
)
LVM - model-based ordination

Perform a model-based unconstrained ordination by fiting a pure latent variable model (package boral - Hui et al., 2014). This will allow to visualize the multivariate stations x species data - similar to nMDS, can be interpreted in the same way.
I’m including a (fixed) row effect to account for differences in site total abundance - this way, the ordination is in terms of species composition.
NB this takes about a million years to run!

lvm.sand <- boral(y = zoo.abnd.flt.sand, 
                  family = "negative.binomial",
                  
                  ## we want to control for site effects - there are 6 sites with 9 replicates each
                  row.eff = "fixed", row.ids = matrix(rep(1:6, each = 9), ncol = 1),  
                  ## 2 latent variables = 2 axes on which to represent the zoobenthic data
                  lv.control = list(num.lv = 2) 
                  
     #              ## example control structure, to check if function does what I want, because otherwise it takes an intolerably long time, and I'll shoot myself if I have to wait for it again
     #              mcmc.control = list(n.burnin = 10, n.iteration = 100,
     # n.thin = 1)
     #              
     
                  )

Check the summary and diagnostic plots for the LVM.

summary(lvm.sand)

## model fit diagnostic plots
plot(lvm.sand) 

The residuals plots look fine (no patterns in the residuals vs fitted, so variance is homogeneous, the quantile plot shows a normal distribution of the residuals) - the model fits the data pretty well.

Save the sand LVM.

write_rds(lvm.sand, 
          here(save.dir, "lvm_sand.RDS"))

Examine the biplot obtained by fitting the LVM, as well as the 20 most “important” species.

lvsplot(lvm.sand, jitter = T, biplot = TRUE, ind.spp = 20)

All in all, the final result resembles the nMDS ordination very much - same 4 clusters (Kraimorie + Chukalya, AKin, Agalina, Sozopol + Paraskeva). Kraimorie and Chukalya are better distinguished on the LVM plot than on the MDS, but still.
The run time is extremely, extremely long (~1h), but the data don’t need to be transformed, and the model fit can be examined and adjusted if necessary.
The species singled out as significant are probably somewhat different - have to check!

Redo the biplot, because this one is not very pretty. I’m not adding the species on top, first because I’m too lazy to figure out the procedure for ordering them, and second because the plot gets too busy.

## extract the LV coordinates of the stations from the model, so that the plot can be redone in ggplot 
lvs.coord.sand <- as_tibble(lvm.sand$lv.median)

## add the stations from the original zoobenthic table (order was not modified)
(lvs.coord.sand <- lvs.coord.sand %>% 
  bind_cols(zoo.abnd.sand %>% select(station))
)

Make the plot and save it.

(plot.lvm.sand <- ggplot(lvs.coord.sand) + 
    geom_point(aes(x = lv1, y = lv2, colour = station)) + 
    scale_color_brewer(palette = "Set2", name = "station", 
                       labels = paste0("S", as.numeric((unique(lvs.coord.sand %>% pull(station)))))) +
   labs(x = "LV1", y = "LV2")
)
## save the LVM plot for the sand stations
ggsave(file = here(figures.dir, "lvm_sand.png"), 
       plot.lvm.sand, 
       width = 15, units = "cm", dpi = 300)
GLM fitting for abundance - environmental data

Let’s fit GLMs to the sites x species matrix to try and explain the observed differences in community structure by the variation of the environmental parameters.
These functions all come from package mvabund.
Import the environmental data - the one cleaned, prepared and saved in the previous notebook (classical multivariate methods). It contains long-term averages for the water column data (2009-2011 + 2013-2014) at each station, repeated for each replicate, and the sediment data (2013-2014), again repeated to the same number of replicates. Only the variables determined to be significant by PCA are kept.

Station is a factor, the rest of the variables are numeric.

Turn the zoobenthic data (minus the all-0 taxa) into a matrix - easier for the mvabund package and methods to deal with.

## there is already one subset of filtered count data (54 x 147) - use it 
zoo.mvabnd.sand <- mvabund(zoo.abnd.flt.sand)
manyGLM by LVM clusters

First, let’s see if the groups from the latent variable model (more or less equal to the clusters from the classical ordination) are valid, and which species exhibit a response.

## construct the vector of the clusters by hand, it's easier that way.. 
lvm.clusters.sand <- c(rep(1, times = 18), rep(2:4, each = 9), rep(3, times = 9))

## convert to factor
(lvm.clusters.sand <- factor(lvm.clusters.sand))

Check the model assumptions. 1. Mean-variance assumption => determines the choice of family parameter. Can be checked by plotting residuals vs fits: if little pattern - the chosen mean-variance assumption is plausible.
Another way: direct plotting (variance ~ mean), for each species within each factor level.

plot(manyglm(zoo.mvabnd.sand ~ lvm.clusters.sand, family = "negative.binomial"))

meanvar.plot(zoo.mvabnd.sand ~ lvm.clusters.sand, table = TRUE)

It’s not perfect, but it’s not too terrible either.

  1. Assumed relationship between mean abundance and environmental variables - link function and formula. When quantitative variables are included in the model (for now, not relevant - will be in the next model) -> if there is a trend in size of residuals at different fitted values (e.g. U-shape,..) = violation of the log-linearity assumption.

Everything looks more or less fine; fit the model.

glms.lvm.sand <- manyglm(zoo.mvabnd.sand ~ lvm.clusters.sand, 
                         family = "negative.binomial")

Explore the fit (residuals, diagnostic plots, etc.).

## residuals vs fitted values
plot(glms.lvm.sand)


## all traditional (g)lm diagnostic plots
plot.manyglm(glms.lvm.sand, which = 1:3)


### source mvabund GLM plotting functions modified to use a grey palette - I just can't redo these plots on my own, the function is doing too complicated things internally to scale the x and y axes
source(here(functions.dir, "default.plot.manyglm_grey.R"))
source(here(functions.dir, "plot.manyglm_grey.R"))

par(mfrow = c(2,2))
lapply(1:3, function(i) plot.manyglm.grey(glms.lvm.sand, which = i, sub.caption = ""))
par(mfrow = c(1, 1))

I really don’t like the rainbow palette, but I would like to include these plots in my thesis results.. Will have to do something about it, just not right now.
Save the model!

write_rds(glms.lvm.sand, 
          here(save.dir, "glms_lvm_sand.RDS"))

Let’s see the model summary (NB takes a LOT of time if there are many resamplings!).

(glms.lvm.sand.summary <- summary(glms.lvm.sand, 
                                  test = "LR", p.uni = "adjusted",
                                  nBoot = 999, ## limit the number of permutations if you just want to check it out
                                  show.time = "all")
)

The factor (here - groups outlined by the LVM) is highly significant according to the models.
This also allows us to see which species exhibit a response to the chosen factor. The LR (likelihood ratio) statistic is used as a measure of the strength of individual taxon contributions to the observed patterns. I’ll save the summary for safekeeping, but I’ll also run an anova - to get an analysis of deviance table on the model fit (also better for extracting the species contributions, or at least I know how to do it).

write_rds(glms.lvm.sand.summary, 
          here(save.dir, "glms_lvm_sand_summary.RDS"))

Run the anova on the model.

(glms.lvm.sand.aov <- anova.manyglm(glms.lvm.sand, 
                                    test = "LR", p.uni = "adjusted", 
                                    nBoot = 999, ## limit the number of permutations for a shorter run time   
                                    show.time = "all") 
)

I probably shouldn’t have printed all this out, but oh well who cares.

Save the ANOVA, too.

write_rds(glms.lvm.sand.aov, 
          here(save.dir, "glms_lvm_sand_anova.RDS"))

NOW let’s get the taxa with the highest contributions to the tested pattern (here - clusters in the LVM, which are really the different soft-bottom habitats).

top_n_sp_glm <- function(glms.aov, tot.dev.expl = 0.75) {
  ## helper retrieving the top n species with the highest contribution to the patterns tested by the GLMs, in decreasing order.
  ## Arguments: glms.aov - results from an ANOVA on the fitted GLMs
  ##            dev.explained - proportion of explained deviance to use as cutoff
  
  ## get the change in deviance due to the tested pattern (= 2nd row from table of univariate test stats), and sort the species in order of decreasing contribution
  uni.sorted <- sort(glms.aov$uni.test[2, ], decreasing = TRUE, index.return = FALSE)

  ## start at 10 species and check how much of the deviance is explained by their contributions. Repeat, increasing by increments of 10 until the desired explained deviance (set at function call) is reached. 
  top.n.sp <- 10
  dev.expl <- sum(uni.sorted[1:top.n.sp])/sum(uni.sorted)
  
  while(dev.expl < tot.dev.expl) {
    top.n.sp <- top.n.sp + 10
    dev.expl <- sum(uni.sorted[1:top.n.sp])/sum(uni.sorted)
  }
  
  ## print the total deviance explained - just for information
  print(paste("Total deviance explained:", round(dev.expl, 3)))
  
  ## return the final top species (and their univariate contributions, just in case) 
  top.sp <- uni.sorted[1:top.n.sp]
  return(top.sp)
}

## get the top contributing species for the initial sand GLMs 
(top.sp.glms.lvm.sand <- top_n_sp_glm(glms.lvm.sand.aov, tot.dev.expl = 0.75)
)

## unfortunately, mvabund likes to rename my species when converting the data to matrix (no spaces in names), and since I'm going to look them up in my initial untransformed count data, I have to change them back..   
names(top.sp.glms.lvm.sand) <- names(top.sp.glms.lvm.sand) %>% 
  str_replace(pattern = "\\.", replacement = " ")

top.sp.glms.lvm.sand

Try to plot these top contributing species - for whatever that’s worth, because 50 species on a plot is a monstrosity.

## get the species and their abundances from the original count data, and transform them to long format
(abnd.top.sp.glms.lvm.sand <- zoo.abnd.sand %>% 
   select(station, names(top.sp.glms.lvm.sand)) %>% 
   gather(key = "species", value = "count", -station) %>% 
   ## turn species into a factor, or you'll be very very sorry later, when they're out of order on the plot. NB need to be in REVERSE order, because ggplot plots from bottom to top, and I want the top-contributing species on top. 
   mutate(species = factor(species, levels = rev(names(top.sp.glms.lvm.sand))))
)
plot_top_n <- function(top.n.sp.data, mapping, labs.legend, lab.y, palette) {
  ## helper for plotting top n species. Was hoping to avoid repeating it from way back when, but no dice. 
  ## Arguments: top.n.sp.data - data frame (long) of top species' counts/biomasses at the different stations
  ##            mapping - mappings of the aesthetics
  ##            labs.legend - labels the use for the legend entries
  ##            lab.y - custom label for y axis
  ##            palette - custom colour palette (for consistency with other plots)
  
  ggplot(top.n.sp.data, mapping) +
    geom_point(alpha = 0.75) + # make points larger & partially transparent
    scale_color_brewer(palette = palette,  labels = labs.legend) + 
    ylab(lab.y) + 
    coord_flip() 
}
(plot.top.sp.glms.lvm.sand <- plot_top_n(abnd.top.sp.glms.lvm.sand,
                                         mapping = aes(x = species, y = log_y_min(count), colour = station),
                                         labs.legend = paste0("S", as.numeric(unique(abnd.top.sp.glms.lvm.sand$station))),
                                         lab.y = "Abundance (log(y/min + 1))",
                                         palette = "Set2"
                                        ) +
    theme(legend.position = "top")
)

Well this is a nightmarish plot.. I’ll probably just put this awfulness in a table and call it a day, or play with lvsplot and the modeled ordination plot, if a plot is what’s needed.

Extract the top-contributing species to each cluster (this same nightmare above, but as a table). This chunk is hopelessly ugly and clumsy (and I’ll have to repeat it for the seagrass, too!), but I’m tired of being stuck on this. I still have many, MANY more things to do, and more time-consuming ones too..

top_sp_glms_table <- function(manyglms.obj.smry, group, p = 0.05) {
  ### extracts the top species in a group for which there is an observed effect in a manyglm test, at the specified probability level.
  ### Returns: tibble with the top species for the specified group/cluster, sorted (descending) by univariate LR value of the species, significant at the given p level. 
  
  ## extract the univariate LR coefficients of the species and their p-values 
  sp_univar <- as_tibble(manyglms.obj.smry$uni.test, rownames = "species")
  sp_p <- as_tibble(manyglms.obj.smry$uni.p, rownames = "species")

  ## combine in the same tibble
  sp_all <- left_join(sp_univar, sp_p, by = "species")  
  
  ## rename the columns
  sp_all <- sp_all %>% 
    rename_at(vars(contains(".x")), list(~str_replace_all(., pattern = ".x", ".LR"))) %>% 
    rename_at(vars(contains(".y")), list(~str_replace_all(., pattern = ".y", ".p")))
  
  ## filter only the group/cluster we want, at the p-level we want
  sp_all_flt <- sp_all %>% 
    select(species, contains(group)) %>% 
    filter_at(vars(contains(".p")), all_vars(. < p)) %>%
    arrange_at(vars(contains(".LR")), list(~desc(.)))

}

top.sp.abnd.glms.lvm.sand <- lapply(names(glms.lvm.sand.summary$aliased), function(x) top_sp_glms_table(glms.lvm.sand.summary, x, p = 0.05)) 

## fix species names (remove dot) 
top.sp.abnd.glms.lvm.sand <- lapply(top.sp.abnd.glms.lvm.sand, function(x) x %>% mutate(species = str_replace(species, pattern = "\\.", replacement = " ")))

## rename columns (= group names) - right now they are something like "lvm.clusters.sand2" etc.
top.sp.abnd.glms.lvm.sand <- lapply(top.sp.abnd.glms.lvm.sand, function(x) x %>% rename_at(vars(contains("lvm.clusters.sand")), list(~str_replace_all(., pattern = "lvm.clusters.sand", "group_"))))

top.sp.abnd.glms.lvm.sand <- lapply(top.sp.abnd.glms.lvm.sand, function(x) x %>% rename_at(vars(contains("Intercept")), list(~str_replace_all(., pattern = "\\(Intercept\\)", "group_1"))))


## pull the abundances from the original count df and add to the summary glm tables 
## make a long df of abundances & add clusters  
zoo.abnd.sand.long <- zoo.abnd.sand %>%
  select(-c(month:replicate)) %>%
  gather(key = "species", value = "count", -station) %>% 
  mutate(group = case_when(station %in% c("Kraimorie", "Chukalya") ~ 1, 
                           station == "Akin" ~ 2, 
                           station %in% c("Sozopol", "Paraskeva") ~ 3, 
                           station == "Agalina" ~ 4))

## sum sp abundances by group; nest by group
zoo.abnd.sand.long.smry <- zoo.abnd.sand.long %>% 
  group_by(species, group) %>% 
  summarise(total_count = sum(count)) %>% 
  group_by(group) %>%
  nest()

## add the counts to the group dfs - wow that's an ugly, ugly hack. Wish I had more time to write this up properly.. 
top.sp.abnd.glms.lvm.sand <- map2(top.sp.abnd.glms.lvm.sand, zoo.abnd.sand.long.smry %>% pull(group), ~left_join(.x, zoo.abnd.sand.long.smry %>% filter(group == .y) %>% unnest(), by = "species"))

## since these are sum counts over all the replicates (that's why the monstrous numbers), average them to be mean counts per group. NB different groups consist of different numbers of replicates, b.c. some groups consist of more than one station
(top.sp.abnd.glms.lvm.sand <- map2(top.sp.abnd.glms.lvm.sand, c(18, 9, 18, 9), function(x, y) x %>% mutate(mean_count = total_count/y))
)

To determine the relative taxon contribution to patterns: LR statistic - a measure of strength of individual taxon contributions. LR expresses how many times more likely the data are under one model than the other. This likelihood ratio, or equivalently its logarithm, can then be used to compute a p-value, or, compared to a critical value, to decide whether to reject the null model in favour of the alternative model.

In this case, the model shows which species exhibit a reaction based on the chosen groups - in other words, which species are more likely to be more/less abundant in each group.
For group 1 (= S1-S2), the species/taxa with significantly higher abundance are: Oligochaeta, H. filiformis, P. kefersteini, M. palmata, P. cirrifera, A. diadema (among others); and the ones with significantly lower abundance - even 0, in some cases - S. bidentata, B.lanceolatum, M. papillicornis, Melita palmata, P. jubatus, and so on.
For group 2 (= S3), the species with higher abundance are: B. lanceolatum, O. limacina, Oligochaeta (this is this strange artifact of 2013), P. kefersteini, L. flavocapitatus. The species with lower abundance are: H. filiformis, A. kagoshimensis, M. stammeri, Melinna palmata, etc. For group 3 (= S4-S6), the species with higher abundance are: C. gallina, L. mediterraneum - with very high dominance over practically all others; also Pseudocuma longicorne, Spio filicornis. The species with lower abundance are: H. filiformis, Oligochaetes (to a certain extent - they are still present, though), A. kagoshimensis, L. koreni, Harmothoe reticulata, Iphinoe tenella, Leiochone leiopygos.
For group 4 (= S5), the species with higher abundance are: Microdeutopus versiculatus, Eurydice dollfusi, Melita palmata, Polygordius neapolitanus, Polycirrus caliendrum, Polycirrus jubatus, Streptosyllis bidentata. The species with lower abundance are: A. kagoshimensis, Melinna palmata, P. cirrifera, P. ciliata, A. alba, I. tenella.
I love how the species with the highest variances (e.g. C. gallina, the most conspicuous example) are consistently pushed back - have lower LR scores. This is very good - C. gallina in particular is dominant in group 3, but is present also in all other groups - its substrate/depth preferences are very wide, so this is not uncommon. It’s not automatically pushed to the top of the list, but its reaction is detected by the manyGLM test. Neat! Contrast to the SIMPER results, where the species with the highest variance are consistently at the top - they contribute the most to the similarity, as per the test definition.

I’m going to save these as separate files (manually), then format them as tables - I know it’s a shame, but I’m too frustrated to figure out how to do it programmatically.
I’ll also put them in a word table in my final text, because I don’t want to deal with a million separate ones (embedded excel tables don’t split over multiple pages).

NB In my text, I’m switching the names/places of group 3 and 4, to be consistent with the SIMPER groups (I’m NOT going to repeat all this just to have the numbers match up). So the file names, table names, etc. remain as above. But in the text, I’ll have the following: group 1 = S1-S2, group 2 = S3, group 3 = S5, group 4 = S4-S6. REMEMBER THIS SO THERE IS NO CONFUSION!

manyGLM by environmental parameters

Now, let’s try to see a different thing - which environmental parameters best describe the species response.
I’m going to use the PCA-filtered environmental data - it’s still going to be a slog, with 7 potential predictors..
First, construct the formula for the model - will do it separately in case I need to update it later, etc.

(formula.env.glms.sand <- formula(paste("zoo.mvabnd.sand ~", 
                                        paste(env.sand %>% select(-station) %>% names(), collapse = "+")))
)
zoo.mvabnd.sand ~ NH4 + NO3 + PO4 + seston + secchi + LUSI + 
    TOM + moisture_content + gravel + silt_clay

Fit the GLMs to the sand abundance data.

env.glms.sand <- manyglm(formula.env.glms.sand,
                         data = env.sand,
                         family = "negative.binomial")

Explore the fit (residuals, diagnostic plots, etc.).

## residuals vs fitted values
plot(env.glms.sand)

## all traditional (g)lm diagnostic plots
plot.manyglm(env.glms.sand, which = 1:3)

# 
# ### source mvabund GLM plotting functions modified to use a grey palette - I just can't redo these plots on my own, the function is doing too complicated things internally to scale the x and y axes
# source(here(functions.dir, "default.plot.manyglm_grey.R"))
# source(here(functions.dir, "plot.manyglm_grey.R"))
# 
# par(mfrow = c(2,2))
# lapply(1:3, function(i) plot.manyglm.grey(glms.lvm.sand, which = i, sub.caption = ""))
# par(mfrow = c(1, 1))

Well, it’s good enough if you ask me (still the kinda strange “line” at lin.pred = -6; otherwise residuals are random enough).

Save the model!

write_rds(env.glms.sand, 
          here(save.dir, "glms_env_sand.RDS"))

Run the anova on the model - I want to see which predictors best explain the species abundance patterns I have. This is one function that would greatly benefit from being run in parallel..

(env.glms.sand.aov <- anova.manyglm(env.glms.sand, 
                                    test = "LR", p.uni = "adjusted", 
                                    nBoot = 999, ## limit the number of permutations for a shorter run time   
                                    show.time = "all") 
)
Resampling begins for test 1.
    Resampling run 0 finished. Time elapsed: 0.01 minutes...
    Resampling run 100 finished. Time elapsed: 1.28 minutes...
    Resampling run 200 finished. Time elapsed: 2.56 minutes...
    Resampling run 300 finished. Time elapsed: 3.83 minutes...
    Resampling run 400 finished. Time elapsed: 5.11 minutes...
    Resampling run 500 finished. Time elapsed: 6.39 minutes...
    Resampling run 600 finished. Time elapsed: 7.66 minutes...
    Resampling run 700 finished. Time elapsed: 8.94 minutes...
    Resampling run 800 finished. Time elapsed: 10.23 minutes...
    Resampling run 900 finished. Time elapsed: 11.49 minutes...
Resampling begins for test 2.
    Resampling run 0 finished. Time elapsed: 0.01 minutes...
    Resampling run 100 finished. Time elapsed: 1.20 minutes...
    Resampling run 200 finished. Time elapsed: 2.39 minutes...
    Resampling run 300 finished. Time elapsed: 3.61 minutes...
    Resampling run 400 finished. Time elapsed: 4.82 minutes...
    Resampling run 500 finished. Time elapsed: 6.05 minutes...
    Resampling run 600 finished. Time elapsed: 7.25 minutes...
    Resampling run 700 finished. Time elapsed: 8.48 minutes...
    Resampling run 800 finished. Time elapsed: 9.68 minutes...
    Resampling run 900 finished. Time elapsed: 10.89 minutes...
Resampling begins for test 3.
    Resampling run 0 finished. Time elapsed: 0.01 minutes...
    Resampling run 100 finished. Time elapsed: 1.18 minutes...
    Resampling run 200 finished. Time elapsed: 2.37 minutes...
    Resampling run 300 finished. Time elapsed: 3.57 minutes...
    Resampling run 400 finished. Time elapsed: 4.75 minutes...
    Resampling run 500 finished. Time elapsed: 5.90 minutes...
    Resampling run 600 finished. Time elapsed: 7.05 minutes...
    Resampling run 700 finished. Time elapsed: 8.21 minutes...
    Resampling run 800 finished. Time elapsed: 9.37 minutes...
    Resampling run 900 finished. Time elapsed: 10.50 minutes...
Resampling begins for test 4.
    Resampling run 0 finished. Time elapsed: 0.01 minutes...
    Resampling run 100 finished. Time elapsed: 1.06 minutes...
    Resampling run 200 finished. Time elapsed: 2.12 minutes...
    Resampling run 300 finished. Time elapsed: 3.19 minutes...
    Resampling run 400 finished. Time elapsed: 4.25 minutes...
    Resampling run 500 finished. Time elapsed: 5.28 minutes...
    Resampling run 600 finished. Time elapsed: 6.31 minutes...
    Resampling run 700 finished. Time elapsed: 7.34 minutes...
    Resampling run 800 finished. Time elapsed: 8.37 minutes...
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Resampling begins for test 5.
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Time elapsed: 1 hr 8 min 48 sec
Analysis of Deviance Table

Model: manyglm(formula = formula.env.glms.sand, family = "negative.binomial", 
Model:     data = env.sand)

Multivariate test:
                 Res.Df Df.diff    Dev Pr(>Dev)    
(Intercept)          53                            
NH4                  52       1 1204.1    0.001 ***
NO3                  51       1  481.4    0.001 ***
PO4                  50       1  659.9    0.001 ***
seston               49       1  486.7    0.001 ***
secchi               48       1  913.4    0.001 ***
LUSI                 47       1   -0.2    0.764    
TOM                  46       1  302.7    0.018 *  
moisture_content     45       1  265.2    0.066 .  
gravel               44       1  294.6    0.046 *  
silt_clay            44       1  297.8    0.558    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Univariate Tests:
                 Abra.alba          Abra.sp.          Acanthocardia.tuberculata         
                       Dev Pr(>Dev)      Dev Pr(>Dev)                       Dev Pr(>Dev)
(Intercept)                                                                             
NH4                  2.178    0.999    1.738    1.000                     3.445    0.987
                  Acari          Actiniaria          Alitta.succinea         
                    Dev Pr(>Dev)        Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                                  
NH4               7.262    0.449      1.738    1.000           1.214    1.000
                 Ampelisca.diadema          Amphibalanus.improvisus          Amphipoda
                               Dev Pr(>Dev)                     Dev Pr(>Dev)       Dev
(Intercept)                                                                           
NH4                          9.971    0.144                  11.111    0.105     0.086
                          Amphitritides.gracilis          Ampithoe.sp.         
                 Pr(>Dev)                    Dev Pr(>Dev)          Dev Pr(>Dev)
(Intercept)                                                                    
NH4                 1.000                  1.382    1.000        0.613    1.000
                 Anadara.kagoshimensis          Aonides.paucibranchiata         
                                   Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                                                                     
NH4                             51.061    0.001                   6.036    0.668
                 Apseudopsis.ostroumovi          Aricidea.claudiae         
                                    Dev Pr(>Dev)               Dev Pr(>Dev)
(Intercept)                                                                
NH4                               0.313    1.000             7.654    0.375
                 Bathyporeia.guilliamsoniana          Bittium.reticulatum         
                                         Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                                                                       
NH4                                    1.783    1.000              31.677    0.001
                 Bodotria.arenosa          Brachynotus.sexdentatus         
                              Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                                                                
NH4                          1.32    1.000                  10.875    0.115
                 Brachystomia.scalaris          Branchiostoma.lanceolatum         
                                   Dev Pr(>Dev)                       Dev Pr(>Dev)
(Intercept)                                                                       
NH4                               1.88    1.000                      0.95    1.000
                 Caecum.armoricum          Caecum.trachea          Capitella.capitata
                              Dev Pr(>Dev)            Dev Pr(>Dev)                Dev
(Intercept)                                                                          
NH4                         5.208    0.751          1.238    1.000              2.301
                          Capitella.minima          Cardiidae          Cerastoderma.edule
                 Pr(>Dev)              Dev Pr(>Dev)       Dev Pr(>Dev)                Dev
(Intercept)                                                                              
NH4                 0.998            5.583    0.709     1.738    1.000              7.532
                          Cerastoderma.glaucum          Chamelea.gallina         
                 Pr(>Dev)                  Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                      
NH4                 0.399                0.714    1.000           40.253    0.001
                 Chondrochelia.savignyi          Crassicorophium.crassicorne         
                                    Dev Pr(>Dev)                         Dev Pr(>Dev)
(Intercept)                                                                          
NH4                               0.656    1.000                       0.046    1.000
                 Cumopsis.goodsir          Cytharella.costulata          Decapoda.larvae
                              Dev Pr(>Dev)                  Dev Pr(>Dev)             Dev
(Intercept)                                                                             
NH4                         3.445    0.987               16.488    0.010           4.145
                          Dinophilus.gyrociliatus          Diogenes.pugilator         
                 Pr(>Dev)                     Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                                           
NH4                 0.885                   2.054    1.000              2.966    0.996
                 Donax.venustus          Elaphognathia.bacescoi          Eteone.flava
                            Dev Pr(>Dev)                    Dev Pr(>Dev)          Dev
(Intercept)                                                                          
NH4                      22.796    0.001                  0.457    1.000            7
                          Eteone.sp.          Eulalia.viridis          Eunice.vittata
                 Pr(>Dev)        Dev Pr(>Dev)             Dev Pr(>Dev)            Dev
(Intercept)                                                                          
NH4                 0.526      2.055    1.000           0.058    1.000          2.984
                          Eurydice.dollfusi          Eurydice.pontica         
                 Pr(>Dev)               Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                   
NH4                 0.996             9.042    0.192            0.015    1.000
                 Exogone.naidina          Gammaridae          Gastrosaccus.sanctus
                             Dev Pr(>Dev)        Dev Pr(>Dev)                  Dev
(Intercept)                                                                       
NH4                        0.422    1.000      0.003    1.000                0.391
                          Genetyllis.tuberculata          Glycera.sp.         
                 Pr(>Dev)                    Dev Pr(>Dev)         Dev Pr(>Dev)
(Intercept)                                                                   
NH4                 1.000                  4.617    0.827        1.83    1.000
                 Glycera.tridactyla          Harmothoe.imbricata         
                                Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                                                              
NH4                           8.031    0.274               7.595    0.389
                 Harmothoe.reticulata          Heteromastus.filiformis          Hirudinea
                                  Dev Pr(>Dev)                     Dev Pr(>Dev)       Dev
(Intercept)                                                                              
NH4                            12.862    0.038                   60.52    0.001     4.652
                          Holothuroidea          Hydrobia.acuta          Hydrobia.sp.
                 Pr(>Dev)           Dev Pr(>Dev)            Dev Pr(>Dev)          Dev
(Intercept)                                                                          
NH4                 0.825         3.138    0.995          3.582    0.971        1.932
                          Iphinoe.sp.          Iphinoe.tenella         
                 Pr(>Dev)         Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                            
NH4                 1.000       0.015    1.000           31.52    0.001
                 Kellia.suborbicularis          Lagis.koreni          Leiochone.leiopygos
                                   Dev Pr(>Dev)          Dev Pr(>Dev)                 Dev
(Intercept)                                                                              
NH4                             10.655    0.131       44.611    0.001              24.389
                          Lentidium.mediterraneum          Leptosynapta.inhaerens
                 Pr(>Dev)                     Dev Pr(>Dev)                    Dev
(Intercept)                                                                      
NH4                 0.001                  37.328    0.001                   2.08
                          Lindrilus.flavocapitatus          Loripes.orbiculatus         
                 Pr(>Dev)                      Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                                                                             
NH4                 0.999                    0.996    1.000              10.096    0.142
                 Lucinella.divaricata          Lysidice.ninetta          Mactra.stultorum
                                  Dev Pr(>Dev)              Dev Pr(>Dev)              Dev
(Intercept)                                                                              
NH4                            27.256    0.001            0.015    1.000            4.196
                          Magelona.papillicornis          Magelona.rosea         
                 Pr(>Dev)                    Dev Pr(>Dev)            Dev Pr(>Dev)
(Intercept)                                                                      
NH4                 0.878                 32.322    0.001          6.909    0.570
                 Maldanidae          Melinna.palmata          Melita.palmata         
                        Dev Pr(>Dev)             Dev Pr(>Dev)            Dev Pr(>Dev)
(Intercept)                                                                          
NH4                   3.445    0.987          85.072    0.001           8.01    0.274
                 Microdeutopus.gryllotalpa          Microdeutopus.sp.         
                                       Dev Pr(>Dev)               Dev Pr(>Dev)
(Intercept)                                                                   
NH4                                  0.009    1.000             3.445    0.987
                 Microdeutopus.versiculatus          Micromaldane.ornithochaeta         
                                        Dev Pr(>Dev)                        Dev Pr(>Dev)
(Intercept)                                                                             
NH4                                    6.59    0.595                     16.373    0.010
                 Micronephthys.stammeri          Microphthalmus.fragilis         
                                    Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                                                                      
NH4                               0.898    1.000                    0.24    1.000
                 Microphthalmus.sp.          Monocorophium.acherusicum         
                                Dev Pr(>Dev)                       Dev Pr(>Dev)
(Intercept)                                                                    
NH4                           6.038    0.668                     8.355    0.240
                 Monocorophium.insidiosum          Mysta.picta         
                                      Dev Pr(>Dev)         Dev Pr(>Dev)
(Intercept)                                                            
NH4                                 7.455    0.409       4.118    0.885
                 Mytilaster.lineatus          Mytilus.galloprovincialis         
                                 Dev Pr(>Dev)                       Dev Pr(>Dev)
(Intercept)                                                                     
NH4                            9.936    0.146                     0.318    1.000
                 Neanthes.sp.          Nemertea          Nephtyidae         
                          Dev Pr(>Dev)      Dev Pr(>Dev)        Dev Pr(>Dev)
(Intercept)                                                                 
NH4                     0.714    1.000    0.249    1.000      3.571    0.982
                 Nephtys.cirrosa          Nereididae          Nereis.pelagica         
                             Dev Pr(>Dev)        Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                                           
NH4                        1.423    1.000      0.015    1.000           0.699    1.000
                 Nereis.perivisceralis          Nereis.pulsatoria         
                                   Dev Pr(>Dev)               Dev Pr(>Dev)
(Intercept)                                                               
NH4                              2.544    0.997             2.262    0.998
                 Nototropis.guttatus          Odostomia.plicata          Oligochaeta
                                 Dev Pr(>Dev)               Dev Pr(>Dev)         Dev
(Intercept)                                                                         
NH4                            0.995    1.000             2.853    0.997        5.97
                          Ophelia.limacina          Papillicardium.papillosum         
                 Pr(>Dev)              Dev Pr(>Dev)                       Dev Pr(>Dev)
(Intercept)                                                                           
NH4                 0.673            0.002    1.000                     3.477    0.987
                 Paradoneis.harpagonea          Parthenina.interstincta         
                                   Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                                                                     
NH4                             15.816    0.012                   1.351    1.000
                 Parvicardium.exiguum          Perinereis.cultrifera         
                                  Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                                  
NH4                             21.34    0.003                 5.282    0.739
                 Perioculodes.longimanus          Pestarella.candida         
                                     Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                                  
NH4                               11.885    0.079              0.457    1.000
                 Pholoe.inornata          Phoronida          Phyllodoce.sp.         
                             Dev Pr(>Dev)       Dev Pr(>Dev)            Dev Pr(>Dev)
(Intercept)                                                                         
NH4                        1.349    1.000    19.848    0.003          0.193    1.000
                 Pisces.larvae          Pisione.remota          Pitar.rudis         
                           Dev Pr(>Dev)            Dev Pr(>Dev)         Dev Pr(>Dev)
(Intercept)                                                                         
NH4                      3.582    0.972          0.002    1.000       2.872    0.997
                 Platyhelminthes          Platynereis.dumerilii         
                             Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                             
NH4                        0.896    1.000                 1.319    1.000
                 Polititapes.aureus          Polychaeta.larvae         
                                Dev Pr(>Dev)               Dev Pr(>Dev)
(Intercept)                                                            
NH4                           3.775    0.907             0.046    1.000
                 Polycirrus.caliendrum          Polycirrus.jubatus         
                                   Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                                
NH4                              4.988    0.783              7.767    0.341
                 Polydora.ciliata          Polygordius.neapolitanus         
                              Dev Pr(>Dev)                      Dev Pr(>Dev)
(Intercept)                                                                 
NH4                        42.608    0.001                    2.208    0.999
                 Prionospio.cirrifera          Protodorvillea.kefersteini         
                                  Dev Pr(>Dev)                        Dev Pr(>Dev)
(Intercept)                                                                       
NH4                            47.902    0.001                      0.422    1.000
                 Protodrilus.sp.          Pseudocuma.longicorne          Rapana.venosa
                             Dev Pr(>Dev)                   Dev Pr(>Dev)           Dev
(Intercept)                                                                           
NH4                        0.059    1.000                22.859    0.001        16.348
                          Retusa.truncatula          Retusa.variabilis         
                 Pr(>Dev)               Dev Pr(>Dev)               Dev Pr(>Dev)
(Intercept)          <NA>              <NA>     <NA>              <NA>     <NA>
NH4                 0.011             1.738    1.000             6.909    0.570
                 Rhithropanopeus.harrisii          Rissoa.membranacea         
                                      Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                          <NA>     <NA>               <NA>     <NA>
NH4                                 0.457    1.000              5.749    0.700
                 Sabellaria.taurica          Salvatoria.clavata         
                                Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                    <NA>     <NA>               <NA>     <NA>
NH4                          16.348    0.011              2.667    0.997
                 Schistomeringos.rudolphi          Sphaerosyllis.hystrix         
                                      Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                          <NA>     <NA>                  <NA>     <NA>
NH4                                  5.67    0.700                 1.732    1.000
                 Spio.filicornis          Spionidae          Spisula.subtruncata         
                             Dev Pr(>Dev)       Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                 <NA>     <NA>      <NA>     <NA>                <NA>     <NA>
NH4                       13.886    0.026     0.322    1.000              38.478    0.001
                 Stenothoe.monoculoides          Sternaspis.scutata         
                                    Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                        <NA>     <NA>               <NA>     <NA>
NH4                               0.457    1.000              0.059    1.000
                 Steromphala.divaricata          Streptosyllis.bidentata         
                                    Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                        <NA>     <NA>                    <NA>     <NA>
NH4                               1.758    1.000                   7.782    0.339
                 Syllis.gracilis          Syllis.hyalina          Tellina.fabula         
                             Dev Pr(>Dev)            Dev Pr(>Dev)            Dev Pr(>Dev)
(Intercept)                 <NA>     <NA>           <NA>     <NA>           <NA>     <NA>
NH4                        0.088    1.000          5.847    0.688          7.655    0.375
                 Tellina.tenuis          Tritia.neritea          Tritia.reticulata
                            Dev Pr(>Dev)            Dev Pr(>Dev)               Dev
(Intercept)                <NA>     <NA>           <NA>     <NA>              <NA>
NH4                       4.644    0.827         21.326    0.003             4.162
                          Turbellaria          Upogebia.pusilla         
                 Pr(>Dev)         Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)          <NA>        <NA>     <NA>             <NA>     <NA>
NH4                 0.885       0.639    1.000            0.457    1.000
 [ reached getOption("max.print") -- omitted 9 rows ]
Arguments:
 Test statistics calculated assuming uncorrelated response (for faster computation) 
P-value calculated using 999 resampling iterations via PIT-trap resampling (to account for correlation in testing.

The results suggest that the long-term average water column parameters have a major influence on the observed community structure; also the sediment TOM, and (marginally) the sediment composition (gravel content).
Save the ANOVA - I really, really don’t want to have to repeat it.

write_rds(env.glms.sand.aov, 
          here(save.dir, "glms_env_sand_anova.RDS"))

Get the taxa with the highest contributions to the tested pattern (here - species most affected by changes in water/environmental quality parameters).

(top.sp.glms.env.sand <- top_n_sp_glm(env.glms.sand.aov, tot.dev.expl = 0.75)
)
[1] "Total deviance explained: 0.783"
           Melinna.palmata    Heteromastus.filiformis      Anadara.kagoshimensis 
                 85.071520                  60.520034                  51.060684 
      Prionospio.cirrifera               Lagis.koreni           Polydora.ciliata 
                 47.902260                  44.610886                  42.608041 
          Chamelea.gallina        Spisula.subtruncata    Lentidium.mediterraneum 
                 40.252681                  38.478437                  37.328312 
    Magelona.papillicornis        Bittium.reticulatum            Iphinoe.tenella 
                 32.322228                  31.676928                  31.519717 
      Lucinella.divaricata        Leiochone.leiopygos      Pseudocuma.longicorne 
                 27.255927                  24.389432                  22.859494 
            Donax.venustus       Parvicardium.exiguum             Tritia.neritea 
                 22.796122                  21.339562                  21.326460 
                 Phoronida       Cytharella.costulata Micromaldane.ornithochaeta 
                 19.847505                  16.488442                  16.372677 
             Rapana.venosa         Sabellaria.taurica      Paradoneis.harpagonea 
                 16.348207                  16.348207                  15.816268 
           Spio.filicornis       Harmothoe.reticulata    Perioculodes.longimanus 
                 13.885810                  12.861565                  11.884939 
   Amphibalanus.improvisus    Brachynotus.sexdentatus      Kellia.suborbicularis 
                 11.110812                  10.875153                  10.654626 
       Loripes.orbiculatus          Ampelisca.diadema        Mytilaster.lineatus 
                 10.096263                   9.971170                   9.935577 
         Eurydice.dollfusi  Monocorophium.acherusicum         Glycera.tridactyla 
                  9.042071                   8.354629                   8.031053 
            Melita.palmata    Streptosyllis.bidentata         Polycirrus.jubatus 
                  8.010391                   7.782071                   7.767249 
            Tellina.fabula 
                  7.655439 

I’m going to plot these top contributing species, but I’m not using the plot. At least this time it’s more manageable, but still not presentable enough..

## get the species and their abundances from the original count data, and transform them to long format
(abnd.top.sp.glms.env.sand <- zoo.abnd.sand %>% 
   select(station, names(top.sp.glms.env.sand)) %>% 
   gather(key = "species", value = "count", -station) %>% 
   ## turn species into a factor, or you'll be very very sorry later, when they're out of order on the plot. NB need to be in REVERSE order, because ggplot plots from bottom to top, and I want the top-contributing species on top. 
   mutate(species = factor(species, levels = rev(names(top.sp.glms.env.sand)))) %>% 
   ## add clusters from LVM as a column
   mutate(group = case_when(station %in% c("Kraimorie", "Chukalya") ~ 1, 
                            station == "Akin" ~ 2, 
                            station %in% c("Sozopol", "Paraskeva") ~ 3, 
                            station == "Agalina" ~ 4))
)
(plot.top.sp.glms.env.sand <- plot_top_n(abnd.top.sp.glms.env.sand,
                                         mapping = aes(x = species, y = log_y_min(count), colour = factor(group)),
                                         group = abnd.top.sp.glms.env.sand %>% pull(group), 
                                         labs.legend = unique(abnd.top.sp.glms.env.sand$group),
                                         lab.y = "Abundance (log(y/min + 1))",
                                         palette = "Set2"
                                        ) + 
    theme(legend.position = "top")
)

Maybe a bit later I’ll try to get this nightmare above as a table…

Final analysis to try: which species respond differently to different environmental parameters? (= traits analysis - fit single predictive model for all species at all sites, but w/o attempting to explain the different responses using traits - the species ID is used in place of a traits matrix).
NB only use the top species that exhibited a reaction in the environmental model fit (= the ones accounting for ~75% of the total variability), and only the significant predictors - to improve run times.

When using LASSO (method = “glm1path”), the algorithm fails to converge - I’m not sure how to interpret it.. Maybe because the function tests each individual species:env.parameter interaction (does it really??), and none of them by themselves are sufficient to explain a species’ response. Not to mention the fact that the samples are not really independent (they are replicates at 6 sites, repeated 3 times).
When using method = “manyglm”, the result is the one shown above. It’s still a bitch to interpret - for example, what is the interpretation of an increase in abundance with both high PO4 and Secchi? Or with high NH4, but low NO3? Where are these conditions ever met?

In fact, everything points towards the conclusion that a species response is determined by a combination of eutrophication parameters in its environment (water column characteristics), and the composition of the sediments (organic matter and granulometry).
This is actually exactly the same thing that the PERMANOVA gives, in this particular case. However, in the future, I’m leaning more towards the modeling approach - it allows you to check the model fit to one’s real data; also, there are no data reductions due to calculation of distance matrices.

Seagrass stations (Burgas Bay, 2013-2014)

Import zoobenthic abundance data (cleaned and prepared).

zoo.abnd.zostera <- read_csv(here(save.dir, "abnd_zostera_orig_clean.csv"))
Parsed with column specification:
cols(
  .default = col_double(),
  station = col_character(),
  habitat = col_character(),
  replicate = col_character()
)
See spec(...) for full column specifications.
## convert station to factor (better safe than sorry later, when the stations are not plotted in the order I want them)
(zoo.abnd.zostera <- zoo.abnd.zostera %>% 
    mutate(station = factor(station, levels = c("Poda", "Otmanli", "Vromos", "Gradina", "Ropotamo")))
)

Remove the all-0 species (= not present in the current dataset).
Maybe also remove the singletons (species appearing only once in the whole dataset and represented by a single individual = so rare that it’s unlikely they carry important information, but it would probably improve the run times).

(zoo.abnd.flt.zostera <- zoo.abnd.zostera %>%
   select(-c(station:replicate)) %>%
   select(which(colSums(.) > 0))
)
LVM - model-based ordination

Perform a model-based unconstrained ordination by fiting a pure latent variable model (package boral - Hui et al., 2014). This will allow to visualize the multivariate stations x species data - similar to nMDS, can be interpreted in the same way.
I’m including a (fixed) row effect to account for differences in site total abundance - this way, the ordination is in terms of species composition.
NB this takes about a million years to run!

lvm.zostera <- boral(y = zoo.abnd.flt.zostera, 
                  family = "negative.binomial",
                  
                  ## we want to control for site effects - there are 6 sites with 9 replicates each
                  row.eff = "fixed", row.ids = matrix(rep(1:5, times = c(8, 8, 4, 8, 4)), ncol = 1),  
                  ## 2 latent variables = 2 axes on which to represent the zoobenthic data
                  lv.control = list(num.lv = 2) 
                  
     #              ## example control structure, to check if function does what I want, because otherwise it takes an intolerably long time, and I'll shoot myself if I have to wait for it again
     #              mcmc.control = list(n.burnin = 10, n.iteration = 100,
     # n.thin = 1)
     #              
     
                  )
module glm loaded
Compiling model graph
   Resolving undeclared variables
   Allocating nodes
Graph information:
   Observed stochastic nodes: 3008
   Unobserved stochastic nodes: 3452
   Total graph size: 21760

Initializing model


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Check the summary and diagnostic plots for the LVM.

summary(lvm.zostera)
$call
boral.default(y = zoo.abnd.flt.zostera, family = "negative.binomial", 
    lv.control = list(num.lv = 2), row.eff = "fixed", row.ids = matrix(rep(1:5, 
        times = c(8, 8, 4, 8, 4)), ncol = 1))

$coefficients
                            coefficients
cols                          beta0 theta1 theta2 Dispersion
  Abra alba                   2.198  1.988  0.000      0.805
  Abra sp.                   -1.608  1.860  0.689     20.217
  Actiniaria                 -2.575  1.839 -0.433     16.301
  Alitta succinea             1.287  2.962 -0.273      5.909
  Ampelisca diadema           3.916  0.203 -2.458      1.892
  Amphibalanus improvisus     1.243  2.972  0.827      1.134
  Ampithoe sp.                0.444  0.910 -1.998     10.014
  Anadara kagoshimensis      -2.476  1.031  2.128     15.707
  Apherusa bispinosa         -2.428 -1.186  0.307     15.831
  Apseudopsis ostroumovi      0.521 -5.653 -2.381      2.029
  Bittium reticulatum         5.338 -2.188  2.471      0.846
  Brachynotus sexdentatus    -1.433  0.672 -0.198     14.885
  Capitella capitata          1.076 -5.388 -0.928      1.170
  Capitella minima            4.479  0.928 -2.812      0.826
  Chamelea gallina           -0.328 -3.872  0.432      0.531
  Chironomidae larvae        -2.276 -2.524 -2.237     11.821
  Cumella limicola            0.896 -4.777 -0.004      0.436
  Cumella pygmaea            -1.927 -2.436  1.321     12.821
  Cytharella costulata       -0.069 -0.433 -0.632      1.365
  Diogenes pugilator         -0.177  0.968 -2.015      0.423
  Eteone flava               -2.885  1.639 -2.341     15.594
  Eunice vittata             -0.779  1.005 -1.601     16.372
  Eurydice dollfusi          -1.465 -2.009  0.879     15.626
  Exogone naidina            -0.462  0.723 -3.254     15.923
  Gastrosaccus sanctus       -2.368 -1.360  0.508     16.826
  Genetyllis tuberculata      0.293  0.005  0.259     10.334
  Glycera sp.                -0.740  2.095  0.024      5.525
  Glycera tridactyla         -1.041  1.003  2.501     12.689
  Glycera unicornis          -2.427  0.849  1.844     15.824
  Harmothoe imbricata        -0.653  0.192  3.196      5.920
  Harmothoe reticulata        0.462  0.415 -0.247      0.958
  Heteromastus filiformis     3.945  0.050  0.370      0.625
  Hirudinea                  -1.133  0.183  0.720     11.083
  Hydrobia acuta             -1.418  2.778 -0.307     21.032
  Hydrobia sp.               -0.577  2.065 -0.426     18.168
  Iphinoe tenella             0.352 -0.093  0.673      6.859
  Kellia suborbicularis      -0.363 -3.112  4.065      3.194
  Lagis koreni                1.062 -0.469  3.133      0.278
  Leiochone leiopygos         0.318 -1.764  3.210      0.498
  Lentidium mediterraneum    -2.097 -2.122  0.080     11.619
  Lepidochitona cinerea      -2.443 -1.418  0.273     15.545
  Loripes orbiculatus         1.922 -2.101  0.408      0.397
  Lucinella divaricata       -1.086 -2.794  0.848     19.669
  Magelona papillicornis     -2.592 -1.498 -0.331     16.872
  Maldane glebifex           -2.507  1.761 -0.177     16.326
  Melinna palmata             0.652  2.694 -1.236      2.709
  Microdeutopus gryllotalpa   1.941  0.402 -2.480      0.546
  Micromaldane ornithochaeta -0.860 -0.847 -1.357     15.169
  Micronephthys stammeri     -1.681  0.374 -1.377     15.521
  Microphthalmus fragilis    -1.199 -0.311  2.808     21.538
  Microphthalmus sp.         -1.678 -4.063 -2.984      5.775
  Monocorophium acherusicum   2.036  2.349 -3.210      1.058
  Mytilaster lineatus         3.458 -2.877 -0.639      1.990
  Mytilus galloprovincialis  -2.440  1.172  2.084     16.400
  Nemertea                    1.885 -0.349  1.128      0.641
  Nephtys cirrosa            -1.858 -1.029  1.939     11.741
  Nephtys kersivalensis      -2.406  0.799  2.018     15.678
  Nereis perivisceralis      -2.437 -1.341  0.676     16.179
  Nereis pulsatoria          -0.673  2.933  1.366     20.309
  Nototropis guttatus         0.552  0.331 -1.833      6.902
  Oligochaeta                 4.784 -1.839  0.190      1.090
  Paradoneis harpagonea      -2.676  2.076 -0.391     15.422
  Parthenina interstincta    -0.088  0.859  3.071     13.948
  Parvicardium exiguum        2.387  0.840 -0.939      1.586
  Perinereis cultrifera       0.507 -0.113 -1.661      6.654
  Perioculodes longimanus    -0.355  1.073 -2.670      1.471
  Phoronida                   0.418 -0.105  0.769      0.983
  Phyllodoce sp.             -3.020  1.597 -2.444     13.608
  Platyhelminthes             0.136  2.049  1.017      5.268
  Platynereis dumerilii       1.160  0.818 -3.257      0.534
  Polititapes aureus         -0.311 -0.003  0.208      8.166
  Polychaeta larvae          -2.476  1.324 -2.128     17.367
  Polydora ciliata            3.321  2.466 -0.944      3.736
  Polygordius neapolitanus   -2.562  1.460 -2.102     16.578
  Prionospio cirrifera        3.661  1.111 -0.632      3.972
  Protodorvillea kefersteini  1.712 -2.163  0.213      2.182
  Pseudocuma longicorne      -1.187  0.060 -0.649     12.114
  Rissoa membranacea          3.074  0.352 -1.468      1.252
  Rissoa splendida           -1.177 -1.453 -3.972      2.213
  Salvatoria clavata         -1.107 -2.064 -4.812      0.653
  Schistomeringos rudolphi    0.407 -1.532  4.380      5.729
  Sphaerosyllis hystrix      -0.252 -3.320  0.508      0.732
  Spio filicornis             1.884  2.108 -2.790      3.201
  Spisula subtruncata        -1.821 -2.397 -0.363      6.609
  Stenosoma capito            1.030 -1.190 -1.260      2.092
  Syllis gracilis             1.417 -2.385  0.383      2.745
  Syllis hyalina             -1.882 -2.749 -2.334     19.788
  Tellina tenuis             -1.540 -1.725  1.252      8.397
  Thracia phaseolina         -2.348 -1.154  0.295     15.251
  Tricolia pullus            -1.550 -3.068 -2.264      1.143
  Tritia neritea             -0.969  1.676 -1.193     14.442
  Tritia reticulata           0.147  0.035  1.052      5.493
  Turbellaria                 0.393  0.927 -0.384     14.925
  Upogebia pusilla           -2.292 -2.751 -2.773     12.546

$lvs
    lv
rows    lv1    lv2
  1   0.633 -0.251
  2   0.719 -0.167
  3   0.561 -0.427
  4   0.552 -0.125
  5   0.310  0.418
  6   0.247  0.446
  7   0.329  0.500
  8   0.410  0.269
  9   0.344 -0.052
  10  0.306  0.058
  11 -0.033 -0.311
  12  0.335  0.063
  13 -0.032  0.438
  14  0.220  0.338
  15  0.073  0.375
  16 -0.139  0.245
  17  0.339 -0.806
  18  0.409 -0.803
  19  0.595 -1.032
  20  0.430 -1.046
  21 -0.544 -0.201
  22 -0.397  0.003
  23 -0.412 -0.046
  24 -0.254  0.022
  25 -0.341 -0.059
  26 -0.433  0.069
  27 -0.508  0.140
  28 -0.513  0.142
  29 -0.474 -0.627
  30 -0.555 -0.633
  31 -0.342 -0.333
  32 -0.474 -0.433

$row.coefficients
$row.coefficients[[1]]
     1      2      3      4      5 
-1.561 -0.963 -2.739 -0.965 -1.000 


$est
[1] "median"

$calc.ics
[1] FALSE

$trial.size
 [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[44] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
[87] 0 0 0 0 0 0 0 0

$num.ord.levels
[1] 0

$prior.control
$prior.control$ssvs.index
[1] -1


attr(,"class")
[1] "summary.boral"
## model fit diagnostic plots
plot(lvm.zostera) 
NULL

The residuals plots look fine (no patterns in the residuals vs fitted, so variance is homogeneous, the quantile plot shows a (more or less) normal distribution of the residuals) - the model fits the data pretty well.

Save the zostera LVM.

write_rds(lvm.zostera, 
          here(save.dir, "lvm_zostera.RDS"))

Examine the biplot obtained by fitting the LVM, as well as the 20 most “important” species.

lvsplot(lvm.zostera, jitter = T, biplot = TRUE, ind.spp = 20)
Only the first 20 ``most important'' latent variable coefficients included in biplot

All in all, the final result resembles the nMDS ordination very much - same stretched clusters (Poda + Otmanli, Vromos pretty much apart, Gradina +- Ropotamo). I don’t see much difference with the nMDS. The main difference seems to be the distance between the 2 years for Poda ana Otmanli - the LVM enlarges it. Have to remember to test for year effect! The run time is actually not that bad for the seagrasses. The species singled out as significant are probably somewhat different - have to check!

Redo the biplot, because this one is not very pretty. I’m not adding the species on top, first because I’m too lazy to figure out the procedure for ordering them, and second because the plot gets too busy.

## extract the LV coordinates of the stations from the model, so that the plot can be redone in ggplot 
lvs.coord.zostera <- as_tibble(lvm.zostera$lv.median)
## add the stations from the original zoobenthic table (order was not modified)
(lvs.coord.zostera <- lvs.coord.zostera %>% 
  bind_cols(zoo.abnd.zostera %>% select(station))
)

Make the plot and save it.

(plot.lvm.zostera <- ggplot(lvs.coord.zostera) + 
    geom_point(aes(x = lv1, y = lv2, colour = station)) + 
    scale_color_brewer(palette = "Set2", name = "station", 
                       labels = paste0("Z", as.numeric((unique(lvs.coord.zostera %>% pull(station)))))) +
   labs(x = "LV1", y = "LV2")
)
ggsave(file = here(figures.dir, "lvm_zostera.png"), 
       plot.lvm.zostera, 
       width = 15, units = "cm", dpi = 300)
Saving 15 x 11.4 cm image

Well, this is a weird one - this plot is flipped around 0 compared to the one that boral’s plotting function gives. Otherwise nothing changes - the spatial relationships between samples are preserved. I suppose it doesn’t matter much - the axes are arbitrary after all, but strange that it happens.

## save the LVM plot for the seagrass
ggsave(file = here(figures.dir, "lvm_zostera.png"), 
       plot.lvm.zostera, 
       width = 15, units = "cm", dpi = 300)
Saving 15 x 17.8 cm image
GLM fitting for abundance - environmental data

Fit GLMs to the sites x species matrix to try and explain the observed differences in community structure by the variation of the environmental parameters.
These functions all come from package mvabund.
Import the environmental data - the one cleaned, prepared and saved in the previous notebook (classical multivariate methods). It contains long-term averages for the water column data (as long-term as available, at least) at each station, repeated for each replicate, the sediment data (2013-2014), and the seagrass data (2013-2014), again repeated to the same number of replicates. Only the variables determined to be significant by PCA are kept.

env.zostera <- read_csv(here(save.dir, "env_data_ordinations_zostera.csv"))
Parsed with column specification:
cols(
  station = col_character(),
  year = col_double(),
  Ntotal = col_double(),
  chl_a = col_double(),
  secchi = col_double(),
  LUSI = col_double(),
  TOM = col_double(),
  moisture_content = col_double(),
  mean_grain_size = col_double(),
  sand = col_double(),
  silt_clay = col_double(),
  shoot_count = col_double(),
  ag_biomass_wet = col_double(),
  bg_biomass_wet = col_double()
)
## convert station to factor
(env.zostera <- env.zostera %>% 
    mutate(station = factor(station,
                            levels = c("Poda", "Otmanli", "Vromos", "Gradina", "Ropotamo")))
)

Station is a factor, the rest of the variables are numeric.

Turn the zoobenthic data (minus the all-0 taxa) into a matrix - easier for the mvabund package and methods to deal with.

## there is already one subset of filtered count data (32 x 94) - use it 
zoo.mvabnd.zostera <- mvabund(zoo.abnd.flt.zostera)
manyGLM by LVM clusters

First, let’s see if the groups from the latent variable model (more or less equal to the clusters from the classical ordination) are valid, and which species exhibit a response.
I’m going to try something new here - 1) loose clusters from the LVM ordination, 1 = Poda-Otmanli, 2 = Vromos, 3 = Gradina-Ropotamo. 2) stations as clusters, as I did before for the seagrass data, although I don’t believe it’s valid/justified to do so… 3) another configuration of clusters from the LVM ordination: 1 = Z1-Z2, 2 = Z3, 3 = Z4, 4 = Z5.

## construct the vectors of the clusters by hand - first, situation 1 above
lvm.clusters.zostera.1 <- rep(1:3, times = c(16, 4, 12))
(lvm.clusters.zostera.1 <- factor(lvm.clusters.zostera.1))
 [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3
Levels: 1 2 3
## again, for case 2
lvm.clusters.zostera.2 <- rep(1:5, times = c(8, 8, 4, 8, 4))
(lvm.clusters.zostera.2 <- factor(lvm.clusters.zostera.2))
 [1] 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3 4 4 4 4 4 4 4 4 5 5 5 5
Levels: 1 2 3 4 5
## again, for case 3
lvm.clusters.zostera.3 <- rep(1:4, times = c(16, 4, 8, 4))
(lvm.clusters.zostera.3 <- factor(lvm.clusters.zostera.3))
 [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4
Levels: 1 2 3 4

LVM clusters - case 1 Check the model assumptions. 1. Mean-variance assumption => determines the choice of family parameter. Can be checked by plotting residuals vs fits: if little pattern - the chosen mean-variance assumption is plausible.
Another way: direct plotting (variance ~ mean), for each species within each factor level.

plot(manyglm(zoo.mvabnd.zostera ~ lvm.clusters.zostera.1, family = "negative.binomial"))

meanvar.plot(zoo.mvabnd.zostera ~ lvm.clusters.zostera.1, table = TRUE)
START SECTION 2 
Plotting if overlay is TRUE
using grouping variable lvm.clusters.zostera.1 105 mean values were 0 and could 
                                        not be included in the log-plot
using grouping variable lvm.clusters.zostera.1 105 variance values were 0 and could not 
                                        be included in the log-plot
FINISHED SECTION 2 
$mean
  Bittium.reticulatum Capitella.minima Oligochaeta Ampelisca.diadema Mytilaster.lineatus
1             57.6875          50.8125     30.0625           6.25000             3.25000
2              0.0000          88.0000      0.7500          80.50000             2.25000
3            183.6667          56.7500     99.5000          23.08333            51.83333
  Heteromastus.filiformis Prionospio.cirrifera Polydora.ciliata Monocorophium.acherusicum
1                17.81250            25.375000        26.562500                  3.937500
2                 2.25000             0.000000         0.000000                 78.250000
3                17.08333             6.666667         3.916667                  1.416667
  Rissoa.membranacea Capitella.capitata Apseudopsis.ostroumovi Spio.filicornis
1           7.437500            0.43750                0.06250       1.4375000
2           9.500000            0.00000                0.00000      38.2500000
3           8.083333           19.83333               18.66667       0.8333333
  Microdeutopus.gryllotalpa Abra.alba Cumella.limicola Loripes.orbiculatus
1                  2.625000  6.312500            0.375            1.125000
2                  4.250000  0.000000            0.000            0.500000
3                  5.916667  1.083333            9.000            7.333333
  Parvicardium.exiguum Protodorvillea.kefersteini Platynereis.dumerilii Nemertea
1             2.812500                       0.75              1.562500 2.375000
2             5.500000                       0.00              9.250000 0.500000
3             2.416667                       7.00              2.333333 2.583333
  Syllis.gracilis Alitta.succinea Amphibalanus.improvisus Stenosoma.capito Lagis.koreni
1           1.625       3.5625000               3.3125000         1.500000    2.1250000
2           0.000       0.0000000               0.2500000         0.000000    0.0000000
3           3.000       0.3333333               0.3333333         1.833333    0.9166667
  Schistomeringos.rudolphi Salvatoria.clavata Leiochone.leiopygos Melinna.palmata
1                1.6875000           0.000000               0.625           0.875
2                0.0000000           1.500000               0.000           2.750
3                0.8333333           2.333333               1.250           0.000
  Microphthalmus.sp. Kellia.suborbicularis Nototropis.guttatus Chamelea.gallina
1           0.000000              0.312500           0.7500000           0.0625
2           0.000000              0.000000           0.0000000           0.0000
3           2.083333              1.583333           0.9166667           1.7500
  Perinereis.cultrifera Sphaerosyllis.hystrix Ampithoe.sp. Harmothoe.reticulata Phoronida
1              0.437500              0.187500    0.1875000            0.7500000 0.5625000
2              0.000000              0.000000    2.7500000            0.0000000 0.0000000
3              1.083333              1.333333    0.3333333            0.4166667 0.5833333
  Perioculodes.longimanus Rissoa.splendida Diogenes.pugilator Iphinoe.tenella
1               0.3750000        0.0000000          0.3750000       0.6875000
2               1.2500000        1.0000000          0.7500000       0.0000000
3               0.3333333        0.9166667          0.4166667       0.1666667
  Platyhelminthes Exogone.naidina Genetyllis.tuberculata Parthenina.interstincta
1       0.6875000       0.0625000                   0.50               0.6250000
2       0.0000000       2.2500000                   0.25               0.0000000
3       0.1666667       0.1666667                   0.25               0.1666667
  Tritia.reticulata Cytharella.costulata Syllis.hyalina Tricolia.pullus Turbellaria
1            0.5625            0.1875000      0.0000000          0.0625       0.375
2            0.0000            0.2500000      0.0000000          0.0000       0.250
3            0.2500            0.5833333      0.8333333          0.7500       0.250
  Harmothoe.imbricata Hydrobia.sp. Lucinella.divaricata Nereis.pulsatoria
1           0.3125000   0.37500000            0.0000000            0.4375
2           0.0000000   0.00000000            0.0000000            0.0000
3           0.1666667   0.08333333            0.5833333            0.0000
  Polititapes.aureus Upogebia.pusilla Glycera.sp. Microphthalmus.fragilis Eunice.vittata
1         0.37500000        0.0000000       0.375                   0.375      0.1875000
2         0.00000000        0.0000000       0.000                   0.000      0.0000000
3         0.08333333        0.5833333       0.000                   0.000      0.1666667
  Glycera.tridactyla Tritia.neritea Chironomidae.larvae Hydrobia.acuta
1             0.3125     0.25000000           0.0000000           0.25
2             0.0000     0.00000000           0.0000000           0.00
3             0.0000     0.08333333           0.3333333           0.00
  Micromaldane.ornithochaeta Cumella.pygmaea Eurydice.dollfusi  Hirudinea
1                       0.00            0.00              0.00 0.12500000
2                       0.25            0.00              0.00 0.00000000
3                       0.25            0.25              0.25 0.08333333
  Pseudocuma.longicorne Spisula.subtruncata Tellina.tenuis Brachynotus.sexdentatus
1             0.0625000                0.00      0.0625000              0.06250000
2             0.0000000                0.00      0.0000000              0.00000000
3             0.1666667                0.25      0.1666667              0.08333333
  Lentidium.mediterraneum Micronephthys.stammeri Nephtys.cirrosa Abra.sp. Actiniaria
1               0.0000000             0.06250000      0.06250000     0.00     0.0625
2               0.0000000             0.00000000      0.00000000     0.25     0.0000
3               0.1666667             0.08333333      0.08333333     0.00     0.0000
  Anadara.kagoshimensis Apherusa.bispinosa Eteone.flava Gastrosaccus.sanctus
1                0.0625         0.00000000         0.00           0.00000000
2                0.0000         0.00000000         0.25           0.00000000
3                0.0000         0.08333333         0.00           0.08333333
  Glycera.unicornis Lepidochitona.cinerea Magelona.papillicornis Maldane.glebifex
1            0.0625            0.00000000             0.00000000           0.0625
2            0.0000            0.00000000             0.00000000           0.0000
3            0.0000            0.08333333             0.08333333           0.0000
  Mytilus.galloprovincialis Nephtys.kersivalensis Nereis.perivisceralis
1                    0.0625                0.0625            0.00000000
2                    0.0000                0.0000            0.00000000
3                    0.0000                0.0000            0.08333333
  Paradoneis.harpagonea Phyllodoce.sp. Polychaeta.larvae Polygordius.neapolitanus
1                0.0625           0.00              0.00                     0.00
2                0.0000           0.25              0.25                     0.25
3                0.0000           0.00              0.00                     0.00
  Thracia.phaseolina
1         0.00000000
2         0.00000000
3         0.08333333

$var
  Bittium.reticulatum Capitella.minima Oligochaeta Ampelisca.diadema Mytilaster.lineatus
1            2642.229         2899.229    700.8625          45.53333           35.000000
2               0.000         3094.000      2.2500         395.00000            1.583333
3           23448.242         3601.295  13116.2727         497.53788         1873.060606
  Heteromastus.filiformis Prionospio.cirrifera Polydora.ciliata Monocorophium.acherusicum
1              177.495833             919.5833       1000.26250                  17.92917
2                1.583333               0.0000          0.00000                3980.91667
3              171.901515             146.9697         38.81061                   2.44697
  Rissoa.membranacea Capitella.capitata Apseudopsis.ostroumovi Spio.filicornis
1          271.72917           1.595833                 0.0625        2.529167
2           11.66667           0.000000                 0.0000      306.250000
3           71.71970         423.606061               537.1515        2.515152
  Microdeutopus.gryllotalpa Abra.alba Cumella.limicola Loripes.orbiculatus
1                  10.78333 24.362500         1.183333            2.383333
2                  16.25000  0.000000         0.000000            1.000000
3                  48.44697  1.356061        29.090909           16.787879
  Parvicardium.exiguum Protodorvillea.kefersteini Platynereis.dumerilii   Nemertea
1            18.829167                    2.60000              6.929167 12.2500000
2             3.666667                    0.00000             32.916667  0.3333333
3             6.265152                   29.27273              5.696970  4.0833333
  Syllis.gracilis Alitta.succinea Amphibalanus.improvisus Stenosoma.capito Lagis.koreni
1            7.45      30.1291667              23.4291667        19.733333    6.5166667
2            0.00       0.0000000               0.2500000         0.000000    0.0000000
3           18.00       0.4242424               0.4242424         6.151515    0.8106061
  Schistomeringos.rudolphi Salvatoria.clavata Leiochone.leiopygos Melinna.palmata
1                 11.29583          0.0000000            0.650000        1.183333
2                  0.00000          0.3333333            0.000000        0.250000
3                  2.69697         13.1515152            3.295455        0.000000
  Microphthalmus.sp. Kellia.suborbicularis Nototropis.guttatus Chamelea.gallina
1            0.00000             0.6291667            1.666667         0.062500
2            0.00000             0.0000000            0.000000         0.000000
3           12.62879            10.0833333            5.356061         1.659091
  Perinereis.cultrifera Sphaerosyllis.hystrix Ampithoe.sp. Harmothoe.reticulata Phoronida
1              2.262500             0.2958333    0.2958333            0.7333333 0.5291667
2              0.000000             0.0000000   11.5833333            0.0000000 0.0000000
3              1.901515             1.6969697    0.4242424            0.8106061 0.8106061
  Perioculodes.longimanus Rissoa.splendida Diogenes.pugilator Iphinoe.tenella
1               0.5166667         0.000000          0.3833333       2.2291667
2               3.5833333         2.000000          0.2500000       0.0000000
3               0.4242424         2.992424          0.4469697       0.3333333
  Platyhelminthes Exogone.naidina Genetyllis.tuberculata Parthenina.interstincta
1       1.4291667       0.0625000              2.2666667               2.6500000
2       0.0000000       8.2500000              0.2500000               0.0000000
3       0.1515152       0.3333333              0.3863636               0.3333333
  Tritia.reticulata Cytharella.costulata Syllis.hyalina Tricolia.pullus Turbellaria
1         1.4625000            0.1625000       0.000000        0.062500        1.05
2         0.0000000            0.2500000       0.000000        0.000000        0.25
3         0.2045455            0.6287879       8.333333        1.477273        0.75
  Harmothoe.imbricata Hydrobia.sp. Lucinella.divaricata Nereis.pulsatoria
1           0.6291667   1.18333333             0.000000            1.4625
2           0.0000000   0.00000000             0.000000            0.0000
3           0.1515152   0.08333333             2.265152            0.0000
  Polititapes.aureus Upogebia.pusilla Glycera.sp. Microphthalmus.fragilis Eunice.vittata
1         0.65000000         0.000000   0.3833333                    2.25      0.2958333
2         0.00000000         0.000000   0.0000000                    0.00      0.0000000
3         0.08333333         2.265152   0.0000000                    0.00      0.3333333
  Glycera.tridactyla Tritia.neritea Chironomidae.larvae Hydrobia.acuta
1          0.6291667     0.60000000           0.0000000              1
2          0.0000000     0.00000000           0.0000000              0
3          0.0000000     0.08333333           0.7878788              0
  Micromaldane.ornithochaeta Cumella.pygmaea Eurydice.dollfusi  Hirudinea
1                  0.0000000       0.0000000         0.0000000 0.11666667
2                  0.2500000       0.0000000         0.0000000 0.00000000
3                  0.3863636       0.3863636         0.3863636 0.08333333
  Pseudocuma.longicorne Spisula.subtruncata Tellina.tenuis Brachynotus.sexdentatus
1             0.0625000           0.0000000      0.0625000              0.06250000
2             0.0000000           0.0000000      0.0000000              0.00000000
3             0.1515152           0.2045455      0.1515152              0.08333333
  Lentidium.mediterraneum Micronephthys.stammeri Nephtys.cirrosa Abra.sp. Actiniaria
1               0.0000000             0.06250000      0.06250000     0.00     0.0625
2               0.0000000             0.00000000      0.00000000     0.25     0.0000
3               0.1515152             0.08333333      0.08333333     0.00     0.0000
  Anadara.kagoshimensis Apherusa.bispinosa Eteone.flava Gastrosaccus.sanctus
1                0.0625         0.00000000         0.00           0.00000000
2                0.0000         0.00000000         0.25           0.00000000
3                0.0000         0.08333333         0.00           0.08333333
  Glycera.unicornis Lepidochitona.cinerea Magelona.papillicornis Maldane.glebifex
1            0.0625            0.00000000             0.00000000           0.0625
2            0.0000            0.00000000             0.00000000           0.0000
3            0.0000            0.08333333             0.08333333           0.0000
  Mytilus.galloprovincialis Nephtys.kersivalensis Nereis.perivisceralis
1                    0.0625                0.0625            0.00000000
2                    0.0000                0.0000            0.00000000
3                    0.0000                0.0000            0.08333333
  Paradoneis.harpagonea Phyllodoce.sp. Polychaeta.larvae Polygordius.neapolitanus
1                0.0625           0.00              0.00                     0.00
2                0.0000           0.25              0.25                     0.25
3                0.0000           0.00              0.00                     0.00
  Thracia.phaseolina
1         0.00000000
2         0.00000000
3         0.08333333

It’s not perfect, but it’s not too terrible either.

  1. Assumed relationship between mean abundance and environmental variables - link function and formula. When quantitative variables are included in the model (for now, not relevant - will be in the next model) -> if there is a trend in size of residuals at different fitted values (e.g. U-shape,..) = violation of the log-linearity assumption.

Everything looks more or less fine; fit the model.

glms.lvm.zostera.1 <- manyglm(zoo.mvabnd.zostera ~ lvm.clusters.zostera.1, 
                              family = "negative.binomial")

Explore the fit (residuals, diagnostic plots, etc.).

## residuals vs fitted values
plot(glms.lvm.zostera.1)

## all traditional (g)lm diagnostic plots
plot.manyglm(glms.lvm.zostera.1, which = 1:3)

# ### source mvabund GLM plotting functions modified to use a grey palette - I just can't redo these plots on my own, the function is doing too complicated things internally to scale the x and y axes
# source(here(functions.dir, "default.plot.manyglm_grey.R"))
# source(here(functions.dir, "plot.manyglm_grey.R"))
# 
# par(mfrow = c(2,2))
# lapply(1:3, function(i) plot.manyglm.grey(glms.lvm.zostera, which = i, sub.caption = ""))
# par(mfrow = c(1, 1))

I really don’t like the rainbow palette, but I would like to include these plots in my thesis results.. Will have to do something about it, just not right now.
Save the model!

write_rds(glms.lvm.zostera.1, 
          here(save.dir, "glms_lvm_zostera_1.RDS"))

Let’s see the model summary (NB takes a LOT of time if there are many resamplings!).

(glms.lvm.zostera.1.summary <- summary(glms.lvm.zostera.1, 
                                  test = "LR", p.uni = "adjusted",
                                  nBoot = 999, ## limit the number of permutations if you just want to check it out
                                  show.time = "all")
)
    Resampling run 0 finished. Time elapsed: 0.00 min ...
    Resampling run 100 finished. Time elapsed: 0.28 min ...
    Resampling run 200 finished. Time elapsed: 0.57 min ...
    Resampling run 300 finished. Time elapsed: 0.85 min ...
    Resampling run 400 finished. Time elapsed: 1.14 min ...
    Resampling run 500 finished. Time elapsed: 1.46 min ...
    Resampling run 600 finished. Time elapsed: 1.74 min ...
    Resampling run 700 finished. Time elapsed: 2.05 min ...
    Resampling run 800 finished. Time elapsed: 2.39 min ...
    Resampling run 900 finished. Time elapsed: 2.70 min ...
Time elapsed: 0 hr 2 min 58 sec

Test statistics:
                        LR value Pr(>LR)    
(Intercept)               1263.9   0.001 ***
lvm.clusters.zostera.12    319.1   0.001 ***
lvm.clusters.zostera.13    386.9   0.001 ***
--- 
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Univariate test statistic: 
                           (Intercept)         lvm.clusters.zostera.12        
                              LR value Pr(>LR)                LR value Pr(>LR)
Abra.alba                       46.653   0.001                  17.680   0.002
Abra.sp.                         6.107   0.514                   3.219   0.648
Actiniaria                       2.833   0.952                   0.446   0.989
Alitta.succinea                  7.171   0.397                   4.935   0.336
Ampelisca.diadema               45.210   0.001                  20.026   0.001
Amphibalanus.improvisus         15.311   0.049                   5.964   0.286
Ampithoe.sp.                     5.196   0.632                   5.826   0.293
Anadara.kagoshimensis            2.833   0.952                   0.446   0.989
Apherusa.bispinosa               4.442   0.795                   0.000   0.998
Apseudopsis.ostroumovi          11.749   0.137                   0.426   0.989
Bittium.reticulatum            156.907   0.001                  24.100   0.001
Brachynotus.sexdentatus          4.472   0.795                   0.446   0.989
Capitella.capitata               2.801   0.952                   2.426   0.768
Capitella.minima               153.136   0.001                   0.735   0.976
Chamelea.gallina                20.892   0.020                   0.446   0.989
Chironomidae.larvae              5.475   0.592                   0.000   1.000
Cumella.limicola                 6.114   0.514                   2.513   0.755
Cumella.pygmaea                  6.270   0.503                   0.000   0.998
Cytharella.costulata            10.234   0.152                   0.059   0.998
Diogenes.pugilator               7.396   0.378                   0.877   0.974
Eteone.flava                     6.107   0.514                   3.219   0.648
Eunice.vittata                   2.143   0.987                   0.865   0.974
Eurydice.dollfusi                6.270   0.503                   0.000   0.998
Exogone.naidina                  5.740   0.564                   5.438   0.297
Gastrosaccus.sanctus             4.442   0.795                   0.000   0.998
Genetyllis.tuberculata           0.906   0.996                   0.171   0.998
Glycera.sp.                      4.780   0.737                   2.664   0.736
Glycera.tridactyla               2.091   0.987                   1.471   0.921
Glycera.unicornis                2.833   0.952                   0.446   0.989
Harmothoe.imbricata              2.901   0.947                   1.687   0.879
Harmothoe.reticulata             0.846   0.996                   4.747   0.360
Heteromastus.filiformis        117.049   0.001                  10.036   0.049
Hirudinea                        5.554   0.582                   0.893   0.974
Hydrobia.acuta                   0.471   0.998                   0.467   0.989
Hydrobia.sp.                     0.891   0.996                   1.130   0.951
Iphinoe.tenella                  0.518   0.998                   2.798   0.705
Kellia.suborbicularis            2.134   0.987                   1.390   0.921
Lagis.koreni                     6.465   0.495                   8.431   0.097
Leiochone.leiopygos              1.439   0.992                   3.585   0.559
Lentidium.mediterraneum          8.262   0.263                   0.000   1.000
Lepidochitona.cinerea            4.442   0.795                   0.000   0.998
Loripes.orbiculatus              0.187   0.998                   1.185   0.939
Lucinella.divaricata             4.632   0.770                   0.000   0.998
Magelona.papillicornis           4.442   0.795                   0.000   0.998
Maldane.glebifex                 2.833   0.952                   0.446   0.989
Melinna.palmata                  0.261   0.998                   6.839   0.191
Microdeutopus.gryllotalpa        9.960   0.163                   0.553   0.989
Micromaldane.ornithochaeta       8.472   0.246                   2.898   0.672
Micronephthys.stammeri           4.472   0.795                   0.446   0.989
Microphthalmus.fragilis          0.234   0.998                   0.467   0.989
Microphthalmus.sp.               7.752   0.352                   0.000   0.998
Monocorophium.acherusicum       26.311   0.010                  26.112   0.001
Mytilaster.lineatus             12.543   0.116                   0.198   0.998
Mytilus.galloprovincialis        2.833   0.952                   0.446   0.989
Nemertea                         8.792   0.238                   3.214   0.648
Nephtys.cirrosa                  4.472   0.795                   0.446   0.989
Nephtys.kersivalensis            2.833   0.952                   0.446   0.989
Nereis.perivisceralis            4.442   0.795                   0.000   0.998
Nereis.pulsatoria                0.491   0.998                   0.980   0.968
Nototropis.guttatus              0.217   0.998                   2.401   0.774
Oligochaeta                    121.705   0.001                  13.320   0.009
Paradoneis.harpagonea            2.833   0.952                   0.446   0.989
Parthenina.interstincta          0.277   0.998                   1.459   0.921
Parvicardium.exiguum            13.759   0.086                   1.460   0.921
Perinereis.cultrifera            1.679   0.992                   1.968   0.853
Perioculodes.longimanus          3.532   0.892                   1.819   0.879
Phoronida                        2.975   0.947                   3.857   0.496
Phyllodoce.sp.                   6.107   0.514                   3.219   0.648
Platyhelminthes                  0.614   0.998                   3.040   0.648
Platynereis.dumerilii            1.732   0.992                   7.023   0.183
Polititapes.aureus               2.721   0.954                   2.061   0.839
Polychaeta.larvae                6.107   0.514                   3.219   0.648
Polydora.ciliata                69.320   0.001                  11.432   0.027
Polygordius.neapolitanus         6.107   0.514                   3.219   0.648
Prionospio.cirrifera            67.239   0.001                  11.104   0.029
Protodorvillea.kefersteini       0.496   0.998                   3.781   0.508
Pseudocuma.longicorne            6.930   0.445                   0.446   0.989
Rissoa.membranacea              49.479   0.001                   0.153   0.998
Rissoa.splendida                13.625   0.088                   8.728   0.086
Salvatoria.clavata              14.949   0.056                  11.446   0.027
Schistomeringos.rudolphi         0.600   0.998                   2.474   0.761
Sphaerosyllis.hystrix           10.204   0.153                   1.307   0.921
Spio.filicornis                  1.529   0.992                  21.365   0.001
Spisula.subtruncata             11.731   0.137                   0.000   1.000
Stenosoma.capito                 0.912   0.996                   4.619   0.371
Syllis.gracilis                  1.237   0.996                   4.542   0.389
Syllis.hyalina                   1.975   0.987                   0.000   1.000
Tellina.tenuis                   6.930   0.445                   0.446   0.989
Thracia.phaseolina               4.442   0.795                   0.000   0.998
Tricolia.pullus                  9.618   0.176                   0.432   0.989
Tritia.neritea                   1.843   0.991                   1.073   0.955
Tritia.reticulata                1.128   0.996                   2.531   0.754
Turbellaria                      1.295   0.996                   0.051   0.998
Upogebia.pusilla                 4.632   0.770                   0.000   1.000
                           lvm.clusters.zostera.13        
                                          LR value Pr(>LR)
Abra.alba                                   15.416   0.010
Abra.sp.                                     0.000   1.000
Actiniaria                                   1.119   1.000
Alitta.succinea                              5.293   0.616
Ampelisca.diadema                            9.548   0.133
Amphibalanus.improvisus                     12.041   0.053
Ampithoe.sp.                                 0.374   1.000
Anadara.kagoshimensis                        1.119   1.000
Apherusa.bispinosa                           1.695   1.000
Apseudopsis.ostroumovi                      26.735   0.001
Bittium.reticulatum                          7.624   0.255
Brachynotus.sexdentatus                      0.041   1.000
Capitella.capitata                          21.010   0.003
Capitella.minima                             0.058   1.000
Chamelea.gallina                            22.405   0.001
Chironomidae.larvae                          3.638   0.907
Cumella.limicola                            26.901   0.001
Cumella.pygmaea                              3.669   0.904
Cytharella.costulata                         2.997   0.965
Diogenes.pugilator                           0.030   1.000
Eteone.flava                                 0.000   1.000
Eunice.vittata                               0.008   1.000
Eurydice.dollfusi                            3.669   0.904
Exogone.naidina                              0.518   1.000
Gastrosaccus.sanctus                         1.695   1.000
Genetyllis.tuberculata                       0.391   1.000
Glycera.sp.                                  6.512   0.407
Glycera.tridactyla                           3.637   0.907
Glycera.unicornis                            1.119   1.000
Harmothoe.imbricata                          0.391   1.000
Harmothoe.reticulata                         1.102   1.000
Heteromastus.filiformis                      0.017   1.000
Hirudinea                                    0.114   1.000
Hydrobia.acuta                               1.163   1.000
Hydrobia.sp.                                 0.826   1.000
Iphinoe.tenella                              2.093   0.991
Kellia.suborbicularis                        2.456   0.983
Lagis.koreni                                 2.825   0.967
Leiochone.leiopygos                          1.600   1.000
Lentidium.mediterraneum                      3.389   0.934
Lepidochitona.cinerea                        1.695   1.000
Loripes.orbiculatus                         21.059   0.003
Lucinella.divaricata                         3.696   0.902
Magelona.papillicornis                       1.695   1.000
Maldane.glebifex                             1.119   1.000
Melinna.palmata                             15.669   0.009
Microdeutopus.gryllotalpa                    3.082   0.961
Micromaldane.ornithochaeta                   4.262   0.794
Micronephthys.stammeri                       0.041   1.000
Microphthalmus.fragilis                      1.163   1.000
Microphthalmus.sp.                           8.208   0.201
Monocorophium.acherusicum                    5.392   0.602
Mytilaster.lineatus                         18.655   0.003
Mytilus.galloprovincialis                    1.119   1.000
Nemertea                                     0.038   1.000
Nephtys.cirrosa                              0.041   1.000
Nephtys.kersivalensis                        1.119   1.000
Nereis.perivisceralis                        1.695   1.000
Nereis.pulsatoria                            2.423   0.984
Nototropis.guttatus                          0.050   1.000
Oligochaeta                                  7.645   0.252
Paradoneis.harpagonea                        1.119   1.000
Parthenina.interstincta                      0.797   1.000
Parvicardium.exiguum                         0.131   1.000
Perinereis.cultrifera                        1.135   1.000
Perioculodes.longimanus                      0.023   1.000
Phoronida                                    0.005   1.000
Phyllodoce.sp.                               0.000   1.000
Platyhelminthes                              2.344   0.987
Platynereis.dumerilii                        0.630   1.000
Polititapes.aureus                           1.865   0.998
Polychaeta.larvae                            0.000   1.000
Polydora.ciliata                             6.959   0.357
Polygordius.neapolitanus                     0.000   1.000
Prionospio.cirrifera                         3.829   0.882
Protodorvillea.kefersteini                  11.945   0.055
Pseudocuma.longicorne                        0.689   1.000
Rissoa.membranacea                           0.036   1.000
Rissoa.splendida                            10.951   0.077
Salvatoria.clavata                          16.907   0.003
Schistomeringos.rudolphi                     0.375   1.000
Sphaerosyllis.hystrix                        9.295   0.147
Spio.filicornis                              1.261   1.000
Spisula.subtruncata                          5.084   0.644
Stenosoma.capito                             0.093   1.000
Syllis.gracilis                              0.821   1.000
Syllis.hyalina                               1.773   1.000
Tellina.tenuis                               0.689   1.000
Thracia.phaseolina                           1.695   1.000
Tricolia.pullus                              6.175   0.457
Tritia.neritea                               0.559   1.000
Tritia.reticulata                            0.825   1.000
Turbellaria                                  0.114   1.000
Upogebia.pusilla                             3.696   0.902

Arguments: with 999 resampling iterations using pit.trap resampling and response assumed to be uncorrelated 

Likelihood Ratio statistic:  703.6, p-value: 0.001 

Univariate test statistic: 
         Abra.alba Abra.sp. Actiniaria Alitta.succinea Ampelisca.diadema
LR value    25.931    4.159      1.386           8.646            20.059
Pr(>LR)      0.001    0.900      0.998           0.323             0.002
         Amphibalanus.improvisus Ampithoe.sp. Anadara.kagoshimensis Apherusa.bispinosa
LR value                  14.882        6.321                 1.386              1.962
Pr(>LR)                    0.030        0.660                 0.998              0.994
         Apseudopsis.ostroumovi Bittium.reticulatum Brachynotus.sexdentatus
LR value                 30.855              31.183                   0.575
Pr(>LR)                   0.001               0.001                   1.000
         Capitella.capitata Capitella.minima Chamelea.gallina Chironomidae.larvae
LR value             26.213            0.739           26.230               4.195
Pr(>LR)               0.001            1.000            0.001               0.891
         Cumella.limicola Cumella.pygmaea Cytharella.costulata Diogenes.pugilator
LR value           32.545           4.228                3.122              0.896
Pr(>LR)             0.001           0.886                0.969              1.000
         Eteone.flava Eunice.vittata Eurydice.dollfusi Exogone.naidina
LR value        4.159          0.871             4.228           5.944
Pr(>LR)         0.900          1.000             0.886           0.694
         Gastrosaccus.sanctus Genetyllis.tuberculata Glycera.sp. Glycera.tridactyla
LR value                1.962                  0.467       7.992              4.484
Pr(>LR)                 0.994                  1.000       0.397              0.851
         Glycera.unicornis Harmothoe.imbricata Harmothoe.reticulata
LR value             1.386               1.841                5.130
Pr(>LR)              0.998               0.994                0.777
         Heteromastus.filiformis Hirudinea Hydrobia.acuta Hydrobia.sp. Iphinoe.tenella
LR value                  10.222     0.915          1.438        1.681           4.160
Pr(>LR)                    0.194     1.000          0.998        0.998           0.895
         Kellia.suborbicularis Lagis.koreni Leiochone.leiopygos Lentidium.mediterraneum
LR value                 4.584        9.705               6.218                   3.923
Pr(>LR)                  0.842        0.226               0.660                   0.918
         Lepidochitona.cinerea Loripes.orbiculatus Lucinella.divaricata
LR value                 1.962              25.259                4.257
Pr(>LR)                  0.994               0.001                0.882
         Magelona.papillicornis Maldane.glebifex Melinna.palmata
LR value                  1.962            1.386          24.203
Pr(>LR)                   0.994            0.998           0.001
         Microdeutopus.gryllotalpa Micromaldane.ornithochaeta Micronephthys.stammeri
LR value                     3.088                      4.544                  0.575
Pr(>LR)                      0.969                      0.848                  1.000
         Microphthalmus.fragilis Microphthalmus.sp. Monocorophium.acherusicum
LR value                   1.437              9.396                    38.329
Pr(>LR)                    0.998              0.260                     0.001
         Mytilaster.lineatus Mytilus.galloprovincialis Nemertea Nephtys.cirrosa
LR value              21.933                     1.386    3.554           0.575
Pr(>LR)                0.001                     0.998    0.941           1.000
         Nephtys.kersivalensis Nereis.perivisceralis Nereis.pulsatoria
LR value                 1.386                 1.962             2.987
Pr(>LR)                  0.998                 0.994             0.969
         Nototropis.guttatus Oligochaeta Paradoneis.harpagonea Parthenina.interstincta
LR value               2.610      21.776                 1.386                   1.965
Pr(>LR)                0.975       0.001                 0.998                   0.994
         Parvicardium.exiguum Perinereis.cultrifera Perioculodes.longimanus Phoronida
LR value                2.086                 3.680                   2.254     4.088
Pr(>LR)                 0.994                 0.941                   0.994     0.905
         Phyllodoce.sp. Platyhelminthes Platynereis.dumerilii Polititapes.aureus
LR value          4.159           4.534                 7.280              3.315
Pr(>LR)           0.900           0.848                 0.498              0.955
         Polychaeta.larvae Polydora.ciliata Polygordius.neapolitanus Prionospio.cirrifera
LR value             4.159           15.690                    4.159               13.193
Pr(>LR)              0.900            0.021                    0.900                0.058
         Protodorvillea.kefersteini Pseudocuma.longicorne Rissoa.membranacea
LR value                     17.536                 1.491              0.158
Pr(>LR)                       0.008                 0.998              1.000
         Rissoa.splendida Salvatoria.clavata Schistomeringos.rudolphi
LR value           11.549             17.003                    2.634
Pr(>LR)             0.111              0.008                    0.975
         Sphaerosyllis.hystrix Spio.filicornis Spisula.subtruncata Stenosoma.capito
LR value                12.713          28.109               5.885            5.011
Pr(>LR)                  0.075           0.001               0.694            0.796
         Syllis.gracilis Syllis.hyalina Tellina.tenuis Thracia.phaseolina Tricolia.pullus
LR value           5.956          2.048          1.491              1.962           7.956
Pr(>LR)            0.694          0.994          0.998              0.994           0.401
         Tritia.neritea Tritia.reticulata Turbellaria Upogebia.pusilla
LR value          1.406             2.932       0.135            4.257
Pr(>LR)           0.998             0.969       1.000            0.882
Arguments:
 Test statistics calculated assuming response assumed to be uncorrelated 
 P-value calculated using 999 resampling iterations via pit.trap resampling (to account for correlation in testing).

The factor is highly significant according to the models.
This also allows us to see which species exhibit a response to the chosen factor. The LR (likelihood ratio) statistic is used as a measure of the strength of individual taxon contributions to the observed patterns. I’ll save the summary for safekeeping, but I’ll also run an anova - to get an analysis of deviance table on the model fit (also better for extracting the species contributions, or at least I know how to do it).

write_rds(glms.lvm.zostera.1.summary, 
          here(save.dir, "glms_lvm_zostera_1_summary.RDS"))

Run the anova on the model.

(glms.lvm.zostera.1.aov <- anova.manyglm(glms.lvm.zostera.1, 
                                    test = "LR", p.uni = "adjusted", 
                                    nBoot = 999, ## limit the number of permutations for a shorter run time   
                                    show.time = "all") 
)
Resampling begins for test 1.
    Resampling run 0 finished. Time elapsed: 0.00 minutes...
    Resampling run 100 finished. Time elapsed: 0.12 minutes...
    Resampling run 200 finished. Time elapsed: 0.24 minutes...
    Resampling run 300 finished. Time elapsed: 0.35 minutes...
    Resampling run 400 finished. Time elapsed: 0.47 minutes...
    Resampling run 500 finished. Time elapsed: 0.58 minutes...
    Resampling run 600 finished. Time elapsed: 0.70 minutes...
    Resampling run 700 finished. Time elapsed: 0.82 minutes...
    Resampling run 800 finished. Time elapsed: 0.93 minutes...
    Resampling run 900 finished. Time elapsed: 1.05 minutes...
Time elapsed: 0 hr 1 min 9 sec
Analysis of Deviance Table

Model: manyglm(formula = zoo.mvabnd.zostera ~ lvm.clusters.zostera.1, 
Model:     family = "negative.binomial")

Multivariate test:
                       Res.Df Df.diff   Dev Pr(>Dev)    
(Intercept)                31                           
lvm.clusters.zostera.1     29       2 703.6    0.001 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Univariate Tests:
                       Abra.alba          Abra.sp.          Actiniaria         
                             Dev Pr(>Dev)      Dev Pr(>Dev)        Dev Pr(>Dev)
(Intercept)                                                                    
lvm.clusters.zostera.1    25.931    0.001    4.159    0.983      1.386    1.000
                       Alitta.succinea          Ampelisca.diadema         
                                   Dev Pr(>Dev)               Dev Pr(>Dev)
(Intercept)                                                               
lvm.clusters.zostera.1           8.646    0.433            20.059    0.006
                       Amphibalanus.improvisus          Ampithoe.sp.         
                                           Dev Pr(>Dev)          Dev Pr(>Dev)
(Intercept)                                                                  
lvm.clusters.zostera.1                  14.882    0.036        6.321    0.799
                       Anadara.kagoshimensis          Apherusa.bispinosa         
                                         Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                                      
lvm.clusters.zostera.1                 1.386    1.000              1.962    1.000
                       Apseudopsis.ostroumovi          Bittium.reticulatum         
                                          Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                                                                        
lvm.clusters.zostera.1                 30.855    0.001              31.183    0.001
                       Brachynotus.sexdentatus          Capitella.capitata         
                                           Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                                        
lvm.clusters.zostera.1                   0.575    1.000             26.213    0.001
                       Capitella.minima          Chamelea.gallina         
                                    Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                               
lvm.clusters.zostera.1            0.739    1.000            26.23    0.001
                       Chironomidae.larvae          Cumella.limicola         
                                       Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                  
lvm.clusters.zostera.1               4.195    0.981           32.545    0.001
                       Cumella.pygmaea          Cytharella.costulata         
                                   Dev Pr(>Dev)                  Dev Pr(>Dev)
(Intercept)                                                                  
lvm.clusters.zostera.1           4.228    0.981                3.122    0.996
                       Diogenes.pugilator          Eteone.flava          Eunice.vittata
                                      Dev Pr(>Dev)          Dev Pr(>Dev)            Dev
(Intercept)                                                                            
lvm.clusters.zostera.1              0.896    1.000        4.159    0.986          0.871
                                Eurydice.dollfusi          Exogone.naidina         
                       Pr(>Dev)               Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                                        
lvm.clusters.zostera.1    1.000             4.228    0.981           5.944    0.838
                       Gastrosaccus.sanctus          Genetyllis.tuberculata         
                                        Dev Pr(>Dev)                    Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.1                1.962    1.000                  0.467    1.000
                       Glycera.sp.          Glycera.tridactyla          Glycera.unicornis
                               Dev Pr(>Dev)                Dev Pr(>Dev)               Dev
(Intercept)                                                                              
lvm.clusters.zostera.1       7.992    0.560              4.484    0.970             1.386
                                Harmothoe.imbricata          Harmothoe.reticulata
                       Pr(>Dev)                 Dev Pr(>Dev)                  Dev
(Intercept)                                                                      
lvm.clusters.zostera.1    1.000               1.841    1.000                 5.13
                                Heteromastus.filiformis          Hirudinea         
                       Pr(>Dev)                     Dev Pr(>Dev)       Dev Pr(>Dev)
(Intercept)                                                                        
lvm.clusters.zostera.1    0.923                  10.222    0.254     0.915    1.000
                       Hydrobia.acuta          Hydrobia.sp.          Iphinoe.tenella
                                  Dev Pr(>Dev)          Dev Pr(>Dev)             Dev
(Intercept)                                                                         
lvm.clusters.zostera.1          1.438    1.000        1.681    1.000            4.16
                                Kellia.suborbicularis          Lagis.koreni         
                       Pr(>Dev)                   Dev Pr(>Dev)          Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.1    0.981                 4.584    0.953        9.705    0.311
                       Leiochone.leiopygos          Lentidium.mediterraneum         
                                       Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.1               6.218    0.803                   3.923    0.986
                       Lepidochitona.cinerea          Loripes.orbiculatus         
                                         Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                                                                       
lvm.clusters.zostera.1                 1.962    1.000              25.259    0.001
                       Lucinella.divaricata          Magelona.papillicornis         
                                        Dev Pr(>Dev)                    Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.1                4.257    0.979                  1.962    1.000
                       Maldane.glebifex          Melinna.palmata         
                                    Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                              
lvm.clusters.zostera.1            1.386    1.000          24.203    0.001
                       Microdeutopus.gryllotalpa          Micromaldane.ornithochaeta
                                             Dev Pr(>Dev)                        Dev
(Intercept)                                                                         
lvm.clusters.zostera.1                     3.088    0.998                      4.544
                                Micronephthys.stammeri          Microphthalmus.fragilis
                       Pr(>Dev)                    Dev Pr(>Dev)                     Dev
(Intercept)                                                                            
lvm.clusters.zostera.1    0.965                  0.575    1.000                   1.437
                                Microphthalmus.sp.          Monocorophium.acherusicum
                       Pr(>Dev)                Dev Pr(>Dev)                       Dev
(Intercept)                                                                          
lvm.clusters.zostera.1    1.000              9.396    0.348                    38.329
                                Mytilaster.lineatus          Mytilus.galloprovincialis
                       Pr(>Dev)                 Dev Pr(>Dev)                       Dev
(Intercept)                                                                           
lvm.clusters.zostera.1    0.001              21.933    0.003                     1.386
                                Nemertea          Nephtys.cirrosa         
                       Pr(>Dev)      Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                               
lvm.clusters.zostera.1    1.000    3.554    0.992           0.575    1.000
                       Nephtys.kersivalensis          Nereis.perivisceralis         
                                         Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.1                 1.386    1.000                 1.962    1.000
                       Nereis.pulsatoria          Nototropis.guttatus         
                                     Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                                                                   
lvm.clusters.zostera.1             2.987    0.999                2.61    1.000
                       Oligochaeta          Paradoneis.harpagonea         
                               Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                               
lvm.clusters.zostera.1      21.776    0.003                 1.386    1.000
                       Parthenina.interstincta          Parvicardium.exiguum         
                                           Dev Pr(>Dev)                  Dev Pr(>Dev)
(Intercept)                                                                          
lvm.clusters.zostera.1                   1.965    1.000                2.086    1.000
                       Perinereis.cultrifera          Perioculodes.longimanus         
                                         Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                                                                           
lvm.clusters.zostera.1                  3.68    0.992                   2.254    1.000
                       Phoronida          Phyllodoce.sp.          Platyhelminthes
                             Dev Pr(>Dev)            Dev Pr(>Dev)             Dev
(Intercept)                                                                      
lvm.clusters.zostera.1     4.088    0.986          4.159    0.986           4.534
                                Platynereis.dumerilii          Polititapes.aureus
                       Pr(>Dev)                   Dev Pr(>Dev)                Dev
(Intercept)                                                                      
lvm.clusters.zostera.1    0.966                  7.28    0.630              3.315
                                Polychaeta.larvae          Polydora.ciliata         
                       Pr(>Dev)               Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.1    0.996             4.159    0.982            15.69    0.031
                       Polygordius.neapolitanus          Prionospio.cirrifera         
                                            Dev Pr(>Dev)                  Dev Pr(>Dev)
(Intercept)                                                                           
lvm.clusters.zostera.1                    4.159    0.982               13.193    0.085
                       Protodorvillea.kefersteini          Pseudocuma.longicorne         
                                              Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                                              
lvm.clusters.zostera.1                     17.536    0.010                 1.491    1.000
                       Rissoa.membranacea          Rissoa.splendida         
                                      Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                 
lvm.clusters.zostera.1              0.158    1.000           11.549    0.153
                       Salvatoria.clavata          Schistomeringos.rudolphi         
                                      Dev Pr(>Dev)                      Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.1             17.003    0.014                    2.634    1.000
                       Sphaerosyllis.hystrix          Spio.filicornis         
                                         Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                                   
lvm.clusters.zostera.1                12.713    0.097          28.109    0.001
                       Spisula.subtruncata          Stenosoma.capito         
                                       Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                  
lvm.clusters.zostera.1               5.885    0.844            5.011    0.923
                       Syllis.gracilis          Syllis.hyalina          Tellina.tenuis
                                   Dev Pr(>Dev)            Dev Pr(>Dev)            Dev
(Intercept)                                                                           
lvm.clusters.zostera.1           5.956    0.838          2.048    1.000          1.491
                                Thracia.phaseolina          Tricolia.pullus         
                       Pr(>Dev)                Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.1    1.000              1.962    1.000           7.956    0.560
                       Tritia.neritea          Tritia.reticulata          Turbellaria
                                  Dev Pr(>Dev)               Dev Pr(>Dev)         Dev
(Intercept)                                                                          
lvm.clusters.zostera.1          1.406    1.000             2.932    0.999       0.135
                                Upogebia.pusilla         
                       Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                              
lvm.clusters.zostera.1    1.000            4.257    0.979
Arguments:
 Test statistics calculated assuming uncorrelated response (for faster computation) 
P-value calculated using 999 resampling iterations via PIT-trap resampling (to account for correlation in testing.

Save the ANOVA, too.

write_rds(glms.lvm.zostera.1.aov, 
          here(save.dir, "glms_lvm_zostera_1_anova.RDS"))

NOW let’s get the taxa with the highest contributions to the tested pattern.

## get the top contributing species for the initial zostera GLMs 
(top.sp.glms.lvm.zostera.1 <- top_n_sp_glm(glms.lvm.zostera.1.aov, tot.dev.expl = 0.75)
)
[1] "Total deviance explained: 0.76"
 Monocorophium.acherusicum           Cumella.limicola        Bittium.reticulatum 
                 38.328670                  32.545296                  31.182981 
    Apseudopsis.ostroumovi            Spio.filicornis           Chamelea.gallina 
                 30.854772                  28.108956                  26.230014 
        Capitella.capitata                  Abra.alba        Loripes.orbiculatus 
                 26.212753                  25.931365                  25.258931 
           Melinna.palmata        Mytilaster.lineatus                Oligochaeta 
                 24.202974                  21.932810                  21.776133 
         Ampelisca.diadema Protodorvillea.kefersteini         Salvatoria.clavata 
                 20.058951                  17.536359                  17.003452 
          Polydora.ciliata    Amphibalanus.improvisus       Prionospio.cirrifera 
                 15.689516                  14.882244                  13.192537 
     Sphaerosyllis.hystrix           Rissoa.splendida    Heteromastus.filiformis 
                 12.713470                  11.548802                  10.221754 
              Lagis.koreni         Microphthalmus.sp.            Alitta.succinea 
                  9.704792                   9.395618                   8.646146 
               Glycera.sp.            Tricolia.pullus      Platynereis.dumerilii 
                  7.992056                   7.955930                   7.279560 
              Ampithoe.sp.        Leiochone.leiopygos            Syllis.gracilis 
                  6.321173                   6.218039                   5.956444 
## unfortunately, mvabund likes to rename my species when converting the data to matrix (no spaces in names), and since I'm going to look them up in my initial untransformed count data, I have to change them back..   
names(top.sp.glms.lvm.zostera.1) <- names(top.sp.glms.lvm.zostera.1) %>% 
  str_replace(pattern = "\\.", replacement = " ")
top.sp.glms.lvm.zostera.1
 Monocorophium acherusicum           Cumella limicola        Bittium reticulatum 
                 38.328670                  32.545296                  31.182981 
    Apseudopsis ostroumovi            Spio filicornis           Chamelea gallina 
                 30.854772                  28.108956                  26.230014 
        Capitella capitata                  Abra alba        Loripes orbiculatus 
                 26.212753                  25.931365                  25.258931 
           Melinna palmata        Mytilaster lineatus                Oligochaeta 
                 24.202974                  21.932810                  21.776133 
         Ampelisca diadema Protodorvillea kefersteini         Salvatoria clavata 
                 20.058951                  17.536359                  17.003452 
          Polydora ciliata    Amphibalanus improvisus       Prionospio cirrifera 
                 15.689516                  14.882244                  13.192537 
     Sphaerosyllis hystrix           Rissoa splendida    Heteromastus filiformis 
                 12.713470                  11.548802                  10.221754 
              Lagis koreni         Microphthalmus sp.            Alitta succinea 
                  9.704792                   9.395618                   8.646146 
               Glycera sp.            Tricolia pullus      Platynereis dumerilii 
                  7.992056                   7.955930                   7.279560 
              Ampithoe sp.        Leiochone leiopygos            Syllis gracilis 
                  6.321173                   6.218039                   5.956444 

Try to plot these top contributing species - for whatever that’s worth, because 50 species on a plot is still a monstrosity.

## get the species and their abundances from the original count data, and transform them to long format
(abnd.top.sp.glms.lvm.zostera.1 <- zoo.abnd.zostera %>% 
   select(station, names(top.sp.glms.lvm.zostera.1)) %>% 
   gather(key = "species", value = "count", -station) %>% 
   ## turn species into a factor, or you'll be very very sorry later, when they're out of order on the plot. NB need to be in REVERSE order, because ggplot plots from bottom to top, and I want the top-contributing species on top. 
   mutate(species = factor(species, levels = rev(names(top.sp.glms.lvm.zostera.1))))
)
(plot.top.sp.glms.lvm.zostera.1 <- plot_top_n(abnd.top.sp.glms.lvm.zostera.1,
                                         mapping = aes(x = species, y = log_y_min(count), colour = station),
                                         labs.legend = paste0("Z", as.numeric(unique(abnd.top.sp.glms.lvm.zostera.1$station))),
                                         lab.y = "Abundance (log(y/min + 1))",
                                         palette = "Set2"
                                        ) +
    theme(legend.position = "top")
)

Well this is a nightmarish plot, but more tolerable than the sand one - there are less species here, so at least it’s readable..

Extract the top-contributing species to each cluster (this same nightmare above, but as a table). This chunk is STILL hopelessly ugly and clumsy.

top.sp.abnd.glms.lvm.zostera.1 <- lapply(names(glms.lvm.zostera.1.summary$aliased), function(x) top_sp_glms_table(glms.lvm.zostera.1.summary, x, p = 0.05)) 
## fix species names (remove dot) 
top.sp.abnd.glms.lvm.zostera.1 <- lapply(top.sp.abnd.glms.lvm.zostera.1, function(x) x %>% mutate(species = str_replace(species, pattern = "\\.", replacement = " ")))
## rename columns (= group names) - right now they are something like "lvm.clusters.zostera2" etc.
top.sp.abnd.glms.lvm.zostera.1 <- lapply(top.sp.abnd.glms.lvm.zostera.1, function(x) x %>% rename_at(vars(contains("lvm.clusters.zostera.1")), list(~str_replace_all(., pattern = "lvm.clusters.zostera.1", "group_"))))
top.sp.abnd.glms.lvm.zostera.1 <- lapply(top.sp.abnd.glms.lvm.zostera.1, function(x) x %>% rename_at(vars(contains("Intercept")), list(~str_replace_all(., pattern = "\\(Intercept\\)", "group_1"))))
## pull the abundances from the original count df and add to the summary glm tables 
## make a long df of abundances & add clusters  
zoo.abnd.zostera.long.1 <- zoo.abnd.zostera %>%
  select(-c(month:replicate)) %>%
  gather(key = "species", value = "count", -station) %>% 
  mutate(group = case_when(station %in% c("Poda", "Otmanli") ~ 1, 
                           station == "Vromos" ~ 2, 
                           station %in% c("Gradina", "Ropotamo") ~ 3)
         )
## sum sp abundances by group; nest by group
zoo.abnd.zostera.long.1.smry <- zoo.abnd.zostera.long.1 %>% 
  group_by(species, group) %>% 
  summarise(total_count = sum(count)) %>% 
  group_by(group) %>%
  nest()
## add the counts to the group dfs - wow that's an ugly, ugly hack. Wish I had more time to write this up properly.. 
top.sp.abnd.glms.lvm.zostera.1 <- map2(top.sp.abnd.glms.lvm.zostera.1, zoo.abnd.zostera.long.1.smry %>% pull(group), ~left_join(.x, zoo.abnd.zostera.long.1.smry %>% filter(group == .y) %>% unnest(), by = "species"))
## since these are sum counts over all the replicates (that's why the monstrous numbers), average them to be mean counts per group. NB different groups consist of different numbers of replicates, b.c. some groups consist of more than one station
(top.sp.abnd.glms.lvm.zostera.1 <- map2(top.sp.abnd.glms.lvm.zostera.1, c(16, 4, 12), function(x, y) x %>% mutate(mean_count = total_count/y))
)
[[1]]

[[2]]

[[3]]
NA

In this case, the model shows which species exhibit a reaction based on the chosen groups - in other words, which species are more likely to be more/less abundant in each group.
I have to say, in the case of the seagrasses and case 1 clusters, there are much fewer species that exhibit a significant response - around 10 for each group.
The LRs are lower for groups 2 and 3 - not sure if this means anything, but for group 1 they are much much higher..
For group 1 (= Z1-Z2), the species/taxa with significantly higher abundance are: Bittium reticulatum, Capitella minima, Oligochaeta, H. filiformis, Polydora ciliata, Prionospio cirrifera, R. membranacea, A. alba, A.diadema, M. acherusicum; and the only one with a significantly lower abundance - Chamelea gallina.
For group 2 (= Z3), the species with higher abundance are: M. acherusicum, S. filicornis, A.dadema. The species with lower abundance are: B. reticulatum, A. alba, Oligochaeta, S. clavata, P. ciliata, P. cirrifera, H. filiformis.
For group 3 (= Z4-Z5), the species with higher abundance are: Cumella limicola, Apseudopsis ostroumovi, Capitella capitata, Mytilaster lineatus, Loripes orbiculatus; less so, but still present - C. gallina, S. clavata. The species with lower abundance are: Abra alba, Melinna palmata (totally absent).

I’ll test each station as its own group, too (as I did before, with the classical multivariate methods) - I’m not sure how much I can trust this grouping (in particular group 3 is a bit far-fetched, if you ask me..).

LVM clusters - case 2 Check the model assumptions.

plot(manyglm(zoo.mvabnd.zostera ~ lvm.clusters.zostera.2, family = "negative.binomial"))

meanvar.plot(zoo.mvabnd.zostera ~ lvm.clusters.zostera.2, table = TRUE)
START SECTION 2 
Plotting if overlay is TRUE
using grouping variable lvm.clusters.zostera.2 215 mean values were 0 and could 
                                        not be included in the log-plot
using grouping variable lvm.clusters.zostera.2 215 variance values were 0 and could not 
                                        be included in the log-plot
FINISHED SECTION 2 
$mean
  Bittium.reticulatum Capitella.minima Oligochaeta Ampelisca.diadema Mytilaster.lineatus
1              56.750           60.000      11.250            10.625               0.750
2              58.625           41.625      48.875             1.875               5.750
3               0.000           88.000       0.750            80.500               2.250
4             238.375           23.125      48.625            24.500              76.375
5              74.250          124.000     201.250            20.250               2.750
  Heteromastus.filiformis Prionospio.cirrifera Polydora.ciliata
1                   8.625                12.50           46.750
2                  27.000                38.25            6.375
3                   2.250                 0.00            0.000
4                  23.000                 0.00            0.250
5                   5.250                20.00           11.250
  Monocorophium.acherusicum Rissoa.membranacea Capitella.capitata Apseudopsis.ostroumovi
1                     3.500              5.375              0.125                  0.000
2                     4.375              9.500              0.750                  0.125
3                    78.250              9.500              0.000                  0.000
4                     1.000             10.125              9.875                  3.875
5                     2.250              4.000             39.750                 48.250
  Spio.filicornis Microdeutopus.gryllotalpa Abra.alba Cumella.limicola
1           1.250                     3.625     6.125             0.00
2           1.625                     1.625     6.500             0.75
3          38.250                     4.250     0.000             0.00
4           1.250                     1.875     0.750            10.25
5           0.000                    14.000     1.750             6.50
  Loripes.orbiculatus Parvicardium.exiguum Protodorvillea.kefersteini
1               0.625                2.625                      0.250
2               1.625                3.000                      1.250
3               0.500                5.500                      0.000
4               8.750                2.875                      9.875
5               4.500                1.500                      1.250
  Platynereis.dumerilii Nemertea Syllis.gracilis Alitta.succinea Amphibalanus.improvisus
1                 1.875    1.000           0.000           7.125                   5.500
2                 1.250    3.750           3.250           0.000                   1.125
3                 9.250    0.500           0.000           0.000                   0.250
4                 1.625    3.125           0.875           0.000                   0.250
5                 3.750    1.500           7.250           1.000                   0.500
  Stenosoma.capito Lagis.koreni Schistomeringos.rudolphi Salvatoria.clavata
1            0.250        0.875                    0.000              0.000
2            2.750        3.375                    3.375              0.000
3            0.000        0.000                    0.000              1.500
4            0.875        1.125                    1.250              0.375
5            3.750        0.500                    0.000              6.250
  Leiochone.leiopygos Melinna.palmata Microphthalmus.sp. Kellia.suborbicularis
1               0.500            0.50              0.000                 0.250
2               0.750            1.25              0.000                 0.375
3               0.000            2.75              0.000                 0.000
4               1.875            0.00              0.625                 2.375
5               0.000            0.00              5.000                 0.000
  Nototropis.guttatus Chamelea.gallina Perinereis.cultrifera Sphaerosyllis.hystrix
1               0.625            0.000                 0.750                 0.000
2               0.875            0.125                 0.125                 0.375
3               0.000            0.000                 0.000                 0.000
4               0.125            2.000                 0.625                 1.375
5               2.500            1.250                 2.000                 1.250
  Ampithoe.sp. Harmothoe.reticulata Phoronida Perioculodes.longimanus Rissoa.splendida
1        0.000                0.250     0.500                   0.375             0.00
2        0.375                1.250     0.625                   0.375             0.00
3        2.750                0.000     0.000                   1.250             1.00
4        0.500                0.125     0.750                   0.125             0.25
5        0.000                1.000     0.250                   0.750             2.25
  Diogenes.pugilator Iphinoe.tenella Platyhelminthes Exogone.naidina
1               0.25           0.125           1.125           0.000
2               0.50           1.250           0.250           0.125
3               0.75           0.000           0.000           2.250
4               0.25           0.250           0.250           0.250
5               0.75           0.000           0.000           0.000
  Genetyllis.tuberculata Parthenina.interstincta Tritia.reticulata Cytharella.costulata
1                  0.000                   1.125             0.000                0.000
2                  1.000                   0.125             1.125                0.375
3                  0.250                   0.000             0.000                0.250
4                  0.375                   0.250             0.250                0.625
5                  0.000                   0.000             0.250                0.500
  Syllis.hyalina Tricolia.pullus Turbellaria Harmothoe.imbricata Hydrobia.sp.
1            0.0           0.000       0.625               0.625        0.750
2            0.0           0.125       0.125               0.000        0.000
3            0.0           0.000       0.250               0.000        0.000
4            0.0           0.250       0.375               0.250        0.125
5            2.5           1.750       0.000               0.000        0.000
  Lucinella.divaricata Nereis.pulsatoria Polititapes.aureus Upogebia.pusilla Glycera.sp.
1                0.000             0.875              0.000             0.00       0.375
2                0.000             0.000              0.750             0.00       0.375
3                0.000             0.000              0.000             0.00       0.000
4                0.875             0.000              0.125             0.00       0.000
5                0.000             0.000              0.000             1.75       0.000
  Microphthalmus.fragilis Eunice.vittata Glycera.tridactyla Tritia.neritea
1                    0.00          0.250              0.125          0.500
2                    0.75          0.125              0.500          0.000
3                    0.00          0.000              0.000          0.000
4                    0.00          0.000              0.000          0.125
5                    0.00          0.500              0.000          0.000
  Chironomidae.larvae Hydrobia.acuta Micromaldane.ornithochaeta Cumella.pygmaea
1                   0            0.5                      0.000           0.000
2                   0            0.0                      0.000           0.000
3                   0            0.0                      0.250           0.000
4                   0            0.0                      0.375           0.375
5                   1            0.0                      0.000           0.000
  Eurydice.dollfusi Hirudinea Pseudocuma.longicorne Spisula.subtruncata Tellina.tenuis
1             0.000     0.125                 0.125                0.00          0.000
2             0.000     0.125                 0.000                0.00          0.125
3             0.000     0.000                 0.000                0.00          0.000
4             0.375     0.125                 0.125                0.25          0.250
5             0.000     0.000                 0.250                0.25          0.000
  Brachynotus.sexdentatus Lentidium.mediterraneum Micronephthys.stammeri Nephtys.cirrosa
1                   0.125                    0.00                  0.125           0.000
2                   0.000                    0.00                  0.000           0.125
3                   0.000                    0.00                  0.000           0.000
4                   0.125                    0.25                  0.000           0.125
5                   0.000                    0.00                  0.250           0.000
  Abra.sp. Actiniaria Anadara.kagoshimensis Apherusa.bispinosa Eteone.flava
1     0.00      0.125                 0.125              0.000         0.00
2     0.00      0.000                 0.000              0.000         0.00
3     0.25      0.000                 0.000              0.000         0.25
4     0.00      0.000                 0.000              0.125         0.00
5     0.00      0.000                 0.000              0.000         0.00
  Gastrosaccus.sanctus Glycera.unicornis Lepidochitona.cinerea Magelona.papillicornis
1                0.000             0.125                 0.000                  0.000
2                0.000             0.000                 0.000                  0.000
3                0.000             0.000                 0.000                  0.000
4                0.125             0.000                 0.125                  0.125
5                0.000             0.000                 0.000                  0.000
  Maldane.glebifex Mytilus.galloprovincialis Nephtys.kersivalensis Nereis.perivisceralis
1            0.125                     0.125                 0.125                 0.000
2            0.000                     0.000                 0.000                 0.000
3            0.000                     0.000                 0.000                 0.000
4            0.000                     0.000                 0.000                 0.125
5            0.000                     0.000                 0.000                 0.000
  Paradoneis.harpagonea Phyllodoce.sp. Polychaeta.larvae Polygordius.neapolitanus
1                 0.125           0.00              0.00                     0.00
2                 0.000           0.00              0.00                     0.00
3                 0.000           0.25              0.25                     0.25
4                 0.000           0.00              0.00                     0.00
5                 0.000           0.00              0.00                     0.00
  Thracia.phaseolina
1              0.000
2              0.000
3              0.000
4              0.125
5              0.000

$var
  Bittium.reticulatum Capitella.minima Oligochaeta Ampelisca.diadema Mytilaster.lineatus
1           4684.5000        4366.8571    49.07143         49.410714            1.928571
2            975.4107        1652.8393   643.83929          4.410714           58.785714
3              0.0000        3094.0000     2.25000        395.000000            1.583333
4          25180.5536         452.6964  3778.26786        735.142857          877.125000
5           3278.2500        3103.3333 18570.91667         92.916667            2.916667
  Heteromastus.filiformis Prionospio.cirrifera Polydora.ciliata
1               77.125000             316.5714     1167.6428571
2              110.285714            1275.0714       44.2678571
3                1.583333               0.0000        0.0000000
4              136.000000               0.0000        0.2142857
5               32.916667             183.3333       34.2500000
  Monocorophium.acherusicum Rissoa.membranacea Capitella.capitata Apseudopsis.ostroumovi
1                 22.000000          12.839286           0.125000               0.000000
2                 15.982143         559.714286           3.071429               0.125000
3               3980.916667          11.666667           0.000000               0.000000
4                  1.428571          95.553571          82.982143               9.839286
5                  4.250000           6.666667         566.250000             196.250000
  Spio.filicornis Microdeutopus.gryllotalpa Abra.alba Cumella.limicola
1        3.357143                 19.410714 13.267857         0.000000
2        1.982143                  1.410714 38.857143         2.214286
3      306.250000                 16.250000  0.000000         0.000000
4        3.357143                  2.696429  1.071429        30.500000
5        0.000000                 40.666667  1.583333        23.000000
  Loripes.orbiculatus Parvicardium.exiguum Protodorvillea.kefersteini
1           0.8392857             7.125000                    0.50000
2           3.6964286            33.142857                    4.50000
3           1.0000000             3.666667                    0.00000
4          16.5000000             8.410714                   16.69643
5           7.0000000             1.666667                    2.25000
  Platynereis.dumerilii   Nemertea Syllis.gracilis Alitta.succinea
1             12.125000  1.7142857        0.000000      35.5535714
2              2.500000 20.2142857        9.928571       0.0000000
3             32.916667  0.3333333        0.000000       0.0000000
4              2.553571  3.8392857        2.982143       0.0000000
5             10.916667  3.6666667       22.916667       0.6666667
  Amphibalanus.improvisus Stenosoma.capito Lagis.koreni Schistomeringos.rudolphi
1              38.0000000        0.2142857    1.5535714                 0.000000
2               1.2678571       38.5000000    8.8392857                17.696429
3               0.2500000        0.0000000    0.0000000                 0.000000
4               0.2142857        0.9821429    0.9821429                 3.642857
5               1.0000000       12.9166667    0.3333333                 0.000000
  Salvatoria.clavata Leiochone.leiopygos Melinna.palmata Microphthalmus.sp.
1          0.0000000           0.5714286       0.5714286              0.000
2          0.0000000           0.7857143       1.6428571              0.000
3          0.3333333           0.0000000       0.2500000              0.000
4          1.1250000           3.8392857       0.0000000              3.125
5         14.9166667           0.0000000       0.0000000             22.000
  Kellia.suborbicularis Nototropis.guttatus Chamelea.gallina Perinereis.cultrifera
1             0.2142857            1.982143         0.000000             4.5000000
2             1.1250000            1.553571         0.125000             0.1250000
3             0.0000000            0.000000         0.000000             0.0000000
4            13.6964286            0.125000         1.714286             0.8392857
5             0.0000000           14.333333         1.583333             3.3333333
  Sphaerosyllis.hystrix Ampithoe.sp. Harmothoe.reticulata Phoronida
1             0.0000000    0.0000000            0.2142857 0.5714286
2             0.5535714    0.5535714            0.7857143 0.5535714
3             0.0000000   11.5833333            0.0000000 0.0000000
4             2.2678571    0.5714286            0.1250000 1.0714286
5             0.9166667    0.0000000            2.0000000 0.2500000
  Perioculodes.longimanus Rissoa.splendida Diogenes.pugilator Iphinoe.tenella
1               0.5535714        0.0000000          0.2142857        0.125000
2               0.5535714        0.0000000          0.5714286        3.928571
3               3.5833333        2.0000000          0.2500000        0.000000
4               0.1250000        0.2142857          0.2142857        0.500000
5               0.9166667        6.9166667          0.9166667        0.000000
  Platyhelminthes Exogone.naidina Genetyllis.tuberculata Parthenina.interstincta
1       2.1250000           0.000              0.0000000                4.982143
2       0.5000000           0.125              4.2857143                0.125000
3       0.0000000           8.250              0.2500000                0.000000
4       0.2142857           0.500              0.5535714                0.500000
5       0.0000000           0.000              0.0000000                0.000000
  Tritia.reticulata Cytharella.costulata Syllis.hyalina Tricolia.pullus Turbellaria
1         0.0000000            0.0000000              0       0.0000000    1.982143
2         2.4107143            0.2678571              0       0.1250000    0.125000
3         0.0000000            0.2500000              0       0.0000000    0.250000
4         0.2142857            0.8392857              0       0.2142857    1.125000
5         0.2500000            0.3333333             25       2.9166667    0.000000
  Harmothoe.imbricata Hydrobia.sp. Lucinella.divaricata Nereis.pulsatoria
1           1.1250000     2.214286             0.000000          2.696429
2           0.0000000     0.000000             0.000000          0.000000
3           0.0000000     0.000000             0.000000          0.000000
4           0.2142857     0.125000             3.267857          0.000000
5           0.0000000     0.000000             0.000000          0.000000
  Polititapes.aureus Upogebia.pusilla Glycera.sp. Microphthalmus.fragilis Eunice.vittata
1           0.000000         0.000000   0.5535714                     0.0          0.500
2           1.071429         0.000000   0.2678571                     4.5          0.125
3           0.000000         0.000000   0.0000000                     0.0          0.000
4           0.125000         0.000000   0.0000000                     0.0          0.000
5           0.000000         5.583333   0.0000000                     0.0          1.000
  Glycera.tridactyla Tritia.neritea Chironomidae.larvae Hydrobia.acuta
1           0.125000       1.142857                   0              2
2           1.142857       0.000000                   0              0
3           0.000000       0.000000                   0              0
4           0.000000       0.125000                   0              0
5           0.000000       0.000000                   2              0
  Micromaldane.ornithochaeta Cumella.pygmaea Eurydice.dollfusi Hirudinea
1                  0.0000000       0.0000000         0.0000000     0.125
2                  0.0000000       0.0000000         0.0000000     0.125
3                  0.2500000       0.0000000         0.0000000     0.000
4                  0.5535714       0.5535714         0.5535714     0.125
5                  0.0000000       0.0000000         0.0000000     0.000
  Pseudocuma.longicorne Spisula.subtruncata Tellina.tenuis Brachynotus.sexdentatus
1                 0.125           0.0000000      0.0000000                   0.125
2                 0.000           0.0000000      0.1250000                   0.000
3                 0.000           0.0000000      0.0000000                   0.000
4                 0.125           0.2142857      0.2142857                   0.125
5                 0.250           0.2500000      0.0000000                   0.000
  Lentidium.mediterraneum Micronephthys.stammeri Nephtys.cirrosa Abra.sp. Actiniaria
1               0.0000000                  0.125           0.000     0.00      0.125
2               0.0000000                  0.000           0.125     0.00      0.000
3               0.0000000                  0.000           0.000     0.25      0.000
4               0.2142857                  0.000           0.125     0.00      0.000
5               0.0000000                  0.250           0.000     0.00      0.000
  Anadara.kagoshimensis Apherusa.bispinosa Eteone.flava Gastrosaccus.sanctus
1                 0.125              0.000         0.00                0.000
2                 0.000              0.000         0.00                0.000
3                 0.000              0.000         0.25                0.000
4                 0.000              0.125         0.00                0.125
5                 0.000              0.000         0.00                0.000
  Glycera.unicornis Lepidochitona.cinerea Magelona.papillicornis Maldane.glebifex
1             0.125                 0.000                  0.000            0.125
2             0.000                 0.000                  0.000            0.000
3             0.000                 0.000                  0.000            0.000
4             0.000                 0.125                  0.125            0.000
5             0.000                 0.000                  0.000            0.000
  Mytilus.galloprovincialis Nephtys.kersivalensis Nereis.perivisceralis
1                     0.125                 0.125                 0.000
2                     0.000                 0.000                 0.000
3                     0.000                 0.000                 0.000
4                     0.000                 0.000                 0.125
5                     0.000                 0.000                 0.000
  Paradoneis.harpagonea Phyllodoce.sp. Polychaeta.larvae Polygordius.neapolitanus
1                 0.125           0.00              0.00                     0.00
2                 0.000           0.00              0.00                     0.00
3                 0.000           0.25              0.25                     0.25
4                 0.000           0.00              0.00                     0.00
5                 0.000           0.00              0.00                     0.00
  Thracia.phaseolina
1              0.000
2              0.000
3              0.000
4              0.125
5              0.000

It’s not perfect, but it’s not too terrible either. I think it’s a little worse than the case 1 fit.

  1. Assumed relationship between mean abundance and environmental variables - link function and formula.

Everything looks more or less fine; fit the model.

glms.lvm.zostera.2 <- manyglm(zoo.mvabnd.zostera ~ lvm.clusters.zostera.2, 
                              family = "negative.binomial")

Explore the fit (residuals, diagnostic plots, etc.).

## residuals vs fitted values
plot(glms.lvm.zostera.2)

## all traditional (g)lm diagnostic plots
plot.manyglm(glms.lvm.zostera.2, which = 1:3)

# ### source mvabund GLM plotting functions modified to use a grey palette - I just can't redo these plots on my own, the function is doing too complicated things internally to scale the x and y axes
# source(here(functions.dir, "default.plot.manyglm_grey.R"))
# source(here(functions.dir, "plot.manyglm_grey.R"))
# 
# par(mfrow = c(2,2))
# lapply(2:3, function(i) plot.manyglm.grey(glms.lvm.zostera, which = i, sub.caption = ""))
# par(mfrow = c(2, 2))

Save the model!

write_rds(glms.lvm.zostera.2, 
          here(save.dir, "glms_lvm_zostera_2.RDS"))

Let’s see the model summary (NB takes a LOT of time if there are many resamplings!).

(glms.lvm.zostera.2.summary <- summary(glms.lvm.zostera.2, 
                                       test = "LR", p.uni = "adjusted",
                                       nBoot = 999, ## limit the number of permutations if you just want to check it out
                                       show.time = "all")
)
    Resampling run 0 finished. Time elapsed: 0.00 min ...
    Resampling run 100 finished. Time elapsed: 0.42 min ...
    Resampling run 200 finished. Time elapsed: 0.84 min ...
    Resampling run 300 finished. Time elapsed: 1.26 min ...
    Resampling run 400 finished. Time elapsed: 1.67 min ...
    Resampling run 500 finished. Time elapsed: 2.09 min ...
    Resampling run 600 finished. Time elapsed: 2.51 min ...
    Resampling run 700 finished. Time elapsed: 2.93 min ...
    Resampling run 800 finished. Time elapsed: 3.35 min ...
    Resampling run 900 finished. Time elapsed: 3.77 min ...
Time elapsed: 0 hr 4 min 11 sec

Test statistics:
                        LR value Pr(>LR)    
(Intercept)               1080.0   0.001 ***
lvm.clusters.zostera.22    256.8   0.001 ***
lvm.clusters.zostera.23    310.9   0.001 ***
lvm.clusters.zostera.24    471.9   0.001 ***
lvm.clusters.zostera.25    346.6   0.001 ***
--- 
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Univariate test statistic: 
                           (Intercept)         lvm.clusters.zostera.22        
                              LR value Pr(>LR)                LR value Pr(>LR)
Abra.alba                       31.096   0.001                   0.023   1.000
Abra.sp.                         4.677   0.714                   0.000   1.000
Actiniaria                       2.341   0.978                   1.386   0.990
Alitta.succinea                 25.658   0.001                  23.057   0.002
Ampelisca.diadema               54.649   0.001                  10.416   0.072
Amphibalanus.improvisus         23.546   0.001                   8.177   0.181
Ampithoe.sp.                     8.217   0.202                   3.482   0.823
Anadara.kagoshimensis            2.341   0.978                   1.386   0.990
Apherusa.bispinosa               3.770   0.854                   0.000   1.000
Apseudopsis.ostroumovi          14.963   0.013                   1.380   0.992
Bittium.reticulatum            126.101   0.001                   0.004   1.000
Brachynotus.sexdentatus          3.387   0.910                   1.386   0.990
Capitella.capitata               5.997   0.502                   2.862   0.912
Capitella.minima               132.041   0.001                   0.433   1.000
Chamelea.gallina                15.617   0.009                   1.386   0.990
Chironomidae.larvae              6.560   0.425                   0.000   1.000
Cumella.limicola                13.674   0.027                   7.694   0.208
Cumella.pygmaea                  5.165   0.620                   0.000   1.000
Cytharella.costulata            12.759   0.036                   4.159   0.675
Diogenes.pugilator               6.380   0.439                   0.680   0.999
Eteone.flava                     4.677   0.714                   0.000   1.000
Eunice.vittata                   1.521   0.992                   0.208   1.000
Eurydice.dollfusi                5.165   0.620                   0.000   1.000
Exogone.naidina                  5.874   0.506                   1.250   0.995
Gastrosaccus.sanctus             3.770   0.854                   0.000   1.000
Genetyllis.tuberculata           6.742   0.398                   5.746   0.444
Glycera.sp.                      2.965   0.944                   0.000   1.000
Glycera.tridactyla               2.776   0.955                   1.033   0.998
Glycera.unicornis                2.341   0.978                   1.386   0.990
Harmothoe.imbricata              0.759   1.000                   5.561   0.476
Harmothoe.reticulata             6.385   0.439                   5.794   0.444
Heteromastus.filiformis         62.249   0.001                  10.679   0.060
Hirudinea                        4.137   0.812                   0.000   1.000
Hydrobia.acuta                   0.171   1.000                   1.494   0.983
Hydrobia.sp.                     0.116   1.000                   3.709   0.788
Iphinoe.tenella                  4.775   0.705                   4.354   0.646
Kellia.suborbicularis            1.985   0.978                   0.104   1.000
Lagis.koreni                     0.095   1.000                   5.999   0.421
Leiochone.leiopygos              1.899   0.978                   0.336   1.000
Lentidium.mediterraneum          6.813   0.388                   0.000   1.000
Lepidochitona.cinerea            3.770   0.854                   0.000   1.000
Loripes.orbiculatus              1.160   0.995                   3.172   0.869
Lucinella.divaricata             3.682   0.861                   0.000   1.000
Magelona.papillicornis           3.770   0.854                   0.000   1.000
Maldane.glebifex                 2.341   0.978                   1.386   0.990
Melinna.palmata                  2.455   0.978                   2.657   0.931
Microdeutopus.gryllotalpa       14.797   0.013                   2.603   0.933
Micromaldane.ornithochaeta       6.542   0.426                   0.000   1.000
Micronephthys.stammeri           3.925   0.837                   1.386   0.990
Microphthalmus.fragilis          1.716   0.983                   1.494   0.983
Microphthalmus.sp.               5.680   0.536                   0.000   1.000
Monocorophium.acherusicum       12.799   0.036                   0.213   1.000
Mytilaster.lineatus              0.385   1.000                  12.953   0.032
Mytilus.galloprovincialis        2.341   0.978                   1.386   0.990
Nemertea                         0.000   1.000                   5.479   0.494
Nephtys.cirrosa                  5.423   0.582                   1.386   0.990
Nephtys.kersivalensis            2.341   0.978                   1.386   0.990
Nereis.perivisceralis            3.770   0.854                   0.000   1.000
Nereis.pulsatoria                0.020   1.000                   3.251   0.853
Nototropis.guttatus              0.402   1.000                   0.116   1.000
Oligochaeta                     58.093   0.001                   9.386   0.110
Paradoneis.harpagonea            2.341   0.978                   1.386   0.990
Parthenina.interstincta          0.017   1.000                   1.662   0.983
Parvicardium.exiguum             6.468   0.429                   0.063   1.000
Perinereis.cultrifera            0.177   1.000                   2.035   0.967
Perioculodes.longimanus          2.180   0.978                   0.000   1.000
Phoronida                        2.237   0.978                   0.110   1.000
Phyllodoce.sp.                   4.677   0.714                   0.000   1.000
Platyhelminthes                  0.058   1.000                   2.602   0.933
Platynereis.dumerilii            1.999   0.978                   0.374   1.000
Polititapes.aureus               9.599   0.112                   6.933   0.288
Polychaeta.larvae                4.677   0.714                   0.000   1.000
Polydora.ciliata                91.477   0.001                  12.416   0.033
Polygordius.neapolitanus         4.677   0.714                   0.000   1.000
Prionospio.cirrifera            49.773   0.001                   4.922   0.568
Protodorvillea.kefersteini       5.371   0.585                   4.879   0.568
Pseudocuma.longicorne            4.585   0.729                   1.386   0.990
Rissoa.membranacea              20.908   0.001                   1.019   0.998
Rissoa.splendida                10.372   0.071                   0.000   1.000
Salvatoria.clavata              14.727   0.013                   0.000   1.000
Schistomeringos.rudolphi         6.673   0.412                   8.799   0.141
Sphaerosyllis.hystrix           12.303   0.039                   4.024   0.720
Spio.filicornis                  0.320   1.000                   0.246   1.000
Spisula.subtruncata              8.280   0.194                   0.000   1.000
Stenosoma.capito                 3.207   0.929                   6.661   0.330
Syllis.gracilis                 11.730   0.042                  17.831   0.005
Syllis.hyalina                   2.396   0.978                   0.000   1.000
Tellina.tenuis                   7.750   0.294                   1.386   0.990
Thracia.phaseolina               3.770   0.854                   0.000   1.000
Tricolia.pullus                 11.452   0.047                   1.380   0.992
Tritia.neritea                   0.707   1.000                   3.479   0.823
Tritia.reticulata                9.399   0.132                   8.301   0.174
Turbellaria                      0.265   1.000                   1.125   0.998
Upogebia.pusilla                 5.886   0.505                   0.000   1.000
                           lvm.clusters.zostera.23         lvm.clusters.zostera.24
                                          LR value Pr(>LR)                LR value
Abra.alba                                   17.297   0.003                  13.450
Abra.sp.                                     2.197   0.783                   0.000
Actiniaria                                   0.811   0.947                   1.386
Alitta.succinea                             15.046   0.008                  23.057
Ampelisca.diadema                           12.759   0.014                   3.426
Amphibalanus.improvisus                     10.584   0.036                  16.614
Ampithoe.sp.                                 9.419   0.062                   4.372
Anadara.kagoshimensis                        0.811   0.947                   1.386
Apherusa.bispinosa                           0.000   1.000                   1.386
Apseudopsis.ostroumovi                       0.000   0.969                  26.746
Bittium.reticulatum                         24.917   0.001                   6.987
Brachynotus.sexdentatus                      0.811   0.947                   0.000
Capitella.capitata                           0.773   0.950                  17.684
Capitella.minima                             0.333   0.969                   2.753
Chamelea.gallina                             0.000   1.000                  19.316
Chironomidae.larvae                          0.000   0.969                   0.000
Cumella.limicola                             0.000   1.000                  31.096
Cumella.pygmaea                              0.000   1.000                   3.167
Cytharella.costulata                         2.197   0.783                   6.931
Diogenes.pugilator                           1.483   0.898                   0.000
Eteone.flava                                 2.197   0.783                   0.000
Eunice.vittata                               1.199   0.898                   2.081
Eurydice.dollfusi                            0.000   1.000                   3.167
Exogone.naidina                              6.160   0.228                   2.262
Gastrosaccus.sanctus                         0.000   1.000                   1.386
Genetyllis.tuberculata                       1.876   0.857                   3.160
Glycera.sp.                                  2.428   0.738                   4.124
Glycera.tridactyla                           0.718   0.958                   1.242
Glycera.unicornis                            0.811   0.947                   1.386
Harmothoe.imbricata                          3.293   0.613                   0.994
Harmothoe.reticulata                         1.622   0.893                   0.340
Heteromastus.filiformis                      7.032   0.170                   8.276
Hirudinea                                    0.811   0.947                   0.000
Hydrobia.acuta                               0.884   0.941                   1.494
Hydrobia.sp.                                 2.194   0.783                   1.407
Iphinoe.tenella                              0.762   0.952                   0.276
Kellia.suborbicularis                        1.257   0.898                   3.343
Lagis.koreni                                 4.950   0.375                   0.180
Leiochone.leiopygos                          3.040   0.670                   4.486
Lentidium.mediterraneum                      0.000   1.000                   2.773
Lepidochitona.cinerea                        0.000   1.000                   1.386
Loripes.orbiculatus                          0.068   0.969                  23.773
Lucinella.divaricata                         0.000   1.000                   3.204
Magelona.papillicornis                       0.000   1.000                   1.386
Maldane.glebifex                             0.811   0.947                   1.386
Melinna.palmata                              9.495   0.062                   5.545
Microdeutopus.gryllotalpa                    0.089   0.969                   1.848
Micromaldane.ornithochaeta                   2.067   0.809                   3.568
Micronephthys.stammeri                       0.811   0.947                   1.386
Microphthalmus.fragilis                      0.000   0.969                   0.000
Microphthalmus.sp.                           0.000   0.969                   3.972
Monocorophium.acherusicum                   20.414   0.002                   4.667
Mytilaster.lineatus                          2.713   0.724                  35.697
Mytilus.galloprovincialis                    0.811   0.947                   1.386
Nemertea                                     0.608   0.958                   4.090
Nephtys.cirrosa                              0.000   1.000                   1.386
Nephtys.kersivalensis                        0.811   0.947                   1.386
Nereis.perivisceralis                        0.000   1.000                   1.386
Nereis.pulsatoria                            1.949   0.850                   3.251
Nototropis.guttatus                          2.528   0.725                   1.537
Oligochaeta                                 11.422   0.027                   9.333
Paradoneis.harpagonea                        0.811   0.947                   1.386
Parthenina.interstincta                      2.228   0.775                   0.968
Parvicardium.exiguum                         1.435   0.898                   0.029
Perinereis.cultrifera                        2.924   0.685                   0.035
Perioculodes.longimanus                      1.591   0.898                   0.850
Phoronida                                    3.210   0.631                   0.396
Phyllodoce.sp.                               2.197   0.783                   0.000
Platyhelminthes                              4.577   0.403                   2.602
Platynereis.dumerilii                        4.688   0.403                   0.049
Polititapes.aureus                           0.000   1.000                   1.367
Polychaeta.larvae                            2.197   0.783                   0.000
Polydora.ciliata                            24.008   0.001                  30.614
Polygordius.neapolitanus                     2.197   0.783                   0.000
Prionospio.cirrifera                        18.028   0.002                  29.724
Protodorvillea.kefersteini                   1.584   0.898                  20.929
Pseudocuma.longicorne                        0.811   0.947                   0.000
Rissoa.membranacea                           0.725   0.958                   1.256
Rissoa.splendida                             7.113   0.167                   2.626
Salvatoria.clavata                          12.384   0.017                   4.104
Schistomeringos.rudolphi                     0.000   1.000                   6.233
Sphaerosyllis.hystrix                        0.000   0.969                  11.891
Spio.filicornis                             19.150   0.002                   0.000
Spisula.subtruncata                          0.000   0.975                   2.773
Stenosoma.capito                             1.424   0.898                   1.680
Syllis.gracilis                              0.000   1.000                   8.039
Syllis.hyalina                               0.000   0.969                   0.000
Tellina.tenuis                               0.000   1.000                   2.773
Thracia.phaseolina                           0.000   1.000                   1.386
Tricolia.pullus                              0.000   0.969                   2.745
Tritia.neritea                               2.051   0.812                   1.033
Tritia.reticulata                            0.000   0.969                   2.586
Turbellaria                                  0.285   0.969                   0.158
Upogebia.pusilla                             0.000   1.000                   0.000
                                   lvm.clusters.zostera.25        
                           Pr(>LR)                LR value Pr(>LR)
Abra.alba                    0.018                   4.346   0.669
Abra.sp.                     1.000                   0.000   1.000
Actiniaria                   0.996                   0.811   0.999
Alitta.succinea              0.002                   6.818   0.295
Ampelisca.diadema            0.806                   1.516   0.991
Amphibalanus.improvisus      0.005                   8.450   0.159
Ampithoe.sp.                 0.642                   0.000   1.000
Anadara.kagoshimensis        0.996                   0.811   0.999
Apherusa.bispinosa           0.995                   0.000   0.999
Apseudopsis.ostroumovi       0.001                  39.178   0.001
Bittium.reticulatum          0.249                   0.201   0.999
Brachynotus.sexdentatus      1.000                   0.811   0.999
Capitella.capitata           0.005                  22.609   0.001
Capitella.minima             0.934                   1.211   0.994
Chamelea.gallina             0.005                  10.986   0.050
Chironomidae.larvae          1.000                   5.456   0.476
Cumella.limicola             0.001                  26.312   0.001
Cumella.pygmaea              0.849                   0.000   1.000
Cytharella.costulata         0.256                   4.394   0.664
Diogenes.pugilator           1.000                   1.483   0.991
Eteone.flava                 1.000                   0.000   1.000
Eunice.vittata               0.983                   0.210   0.999
Eurydice.dollfusi            0.849                   0.000   0.999
Exogone.naidina              0.972                   0.000   0.999
Gastrosaccus.sanctus         0.996                   0.000   1.000
Genetyllis.tuberculata       0.850                   0.000   1.000
Glycera.sp.                  0.721                   2.428   0.938
Glycera.tridactyla           0.997                   0.718   0.999
Glycera.unicornis            0.996                   0.811   0.999
Harmothoe.imbricata          0.998                   3.293   0.805
Harmothoe.reticulata         1.000                   2.773   0.880
Heteromastus.filiformis      0.172                   1.330   0.994
Hirudinea                    1.000                   0.811   0.999
Hydrobia.acuta               0.993                   0.884   0.999
Hydrobia.sp.                 0.995                   2.194   0.953
Iphinoe.tenella              1.000                   0.762   0.999
Kellia.suborbicularis        0.818                   1.257   0.994
Lagis.koreni                 1.000                   0.420   0.999
Leiochone.leiopygos          0.624                   3.040   0.837
Lentidium.mediterraneum      0.921                   0.000   1.000
Lepidochitona.cinerea        0.995                   0.000   1.000
Loripes.orbiculatus          0.002                  12.893   0.023
Lucinella.divaricata         0.844                   0.000   1.000
Magelona.papillicornis       0.996                   0.000   1.000
Maldane.glebifex             0.996                   0.811   0.999
Melinna.palmata              0.470                   3.244   0.807
Microdeutopus.gryllotalpa    0.989                   6.470   0.331
Micromaldane.ornithochaeta   0.786                   0.000   1.000
Micronephthys.stammeri       0.995                   0.236   0.999
Microphthalmus.fragilis      1.000                   0.000   1.000
Microphthalmus.sp.           0.731                   7.235   0.253
Monocorophium.acherusicum    0.605                   0.479   0.999
Mytilaster.lineatus          0.001                   3.994   0.738
Mytilus.galloprovincialis    0.996                   0.811   0.999
Nemertea                     0.722                   0.324   0.999
Nephtys.cirrosa              0.995                   0.000   0.999
Nephtys.kersivalensis        0.996                   0.811   0.999
Nereis.perivisceralis        0.996                   0.000   1.000
Nereis.pulsatoria            0.831                   1.949   0.972
Nototropis.guttatus          0.992                   1.502   0.991
Oligochaeta                  0.100                  21.743   0.001
Paradoneis.harpagonea        0.996                   0.811   0.999
Parthenina.interstincta      0.998                   2.228   0.951
Parvicardium.exiguum         1.000                   0.610   0.999
Perinereis.cultrifera        1.000                   0.836   0.999
Perioculodes.longimanus      0.998                   0.467   0.999
Phoronida                    1.000                   0.433   0.999
Phyllodoce.sp.               1.000                   0.000   1.000
Platyhelminthes              0.954                   4.577   0.632
Platynereis.dumerilii        1.000                   0.899   0.999
Polititapes.aureus           0.996                   0.000   1.000
Polychaeta.larvae            1.000                   0.000   1.000
Polydora.ciliata             0.001                   5.015   0.546
Polygordius.neapolitanus     1.000                   0.000   1.000
Prionospio.cirrifera         0.001                   0.688   0.999
Protodorvillea.kefersteini   0.004                   3.630   0.780
Pseudocuma.longicorne        1.000                   0.236   0.999
Rissoa.membranacea           0.997                   0.171   0.999
Rissoa.splendida             0.950                  11.194   0.047
Salvatoria.clavata           0.722                  23.844   0.001
Schistomeringos.rudolphi     0.366                   0.000   0.999
Sphaerosyllis.hystrix        0.026                   9.470   0.103
Spio.filicornis              1.000                   6.560   0.319
Spisula.subtruncata          0.921                   2.197   0.953
Stenosoma.capito             0.989                   7.067   0.269
Syllis.gracilis              0.175                  21.341   0.001
Syllis.hyalina               1.000                   2.507   0.929
Tellina.tenuis               0.931                   0.000   1.000
Thracia.phaseolina           0.995                   0.000   0.999
Tricolia.pullus              0.934                  11.106   0.048
Tritia.neritea               0.998                   2.051   0.963
Tritia.reticulata            0.954                   2.073   0.961
Turbellaria                  1.000                   2.003   0.967
Upogebia.pusilla             1.000                   5.769   0.409

Arguments: with 999 resampling iterations using pit.trap resampling and response assumed to be uncorrelated 

Likelihood Ratio statistic:   1223, p-value: 0.001 

Univariate test statistic: 
         Abra.alba Abra.sp. Actiniaria Alitta.succinea Ampelisca.diadema
LR value    27.461    4.159      2.773          36.585            30.570
Pr(>LR)      0.002    0.961      0.981           0.001             0.001
         Amphibalanus.improvisus Ampithoe.sp. Anadara.kagoshimensis Apherusa.bispinosa
LR value                  23.408       12.209                 2.773              2.773
Pr(>LR)                    0.008        0.282                 0.981              0.981
         Apseudopsis.ostroumovi Bittium.reticulatum Brachynotus.sexdentatus
LR value                 52.794              34.193                   2.773
Pr(>LR)                   0.001               0.001                   0.981
         Capitella.capitata Capitella.minima Chamelea.gallina Chironomidae.larvae
LR value             33.199            7.227           28.525               9.651
Pr(>LR)               0.001            0.781            0.001               0.513
         Cumella.limicola Cumella.pygmaea Cytharella.costulata Diogenes.pugilator
LR value           41.328           6.118                7.354              3.059
Pr(>LR)             0.001           0.840                0.775              0.981
         Eteone.flava Eunice.vittata Eurydice.dollfusi Exogone.naidina
LR value        4.159          3.779             6.118           8.477
Pr(>LR)         0.961          0.967             0.840           0.642
         Gastrosaccus.sanctus Genetyllis.tuberculata Glycera.sp. Glycera.tridactyla
LR value                2.773                  7.712       7.992              5.516
Pr(>LR)                 0.981                  0.739       0.704              0.903
         Glycera.unicornis Harmothoe.imbricata Harmothoe.reticulata
LR value             2.773               8.753               15.210
Pr(>LR)              0.981               0.597                0.093
         Heteromastus.filiformis Hirudinea Hydrobia.acuta Hydrobia.sp. Iphinoe.tenella
LR value                  28.142     1.726          2.932        5.959           9.824
Pr(>LR)                    0.002     0.981          0.981        0.860           0.484
         Kellia.suborbicularis Lagis.koreni Leiochone.leiopygos Lentidium.mediterraneum
LR value                 9.077       16.471              15.331                   5.545
Pr(>LR)                  0.579        0.076               0.091                   0.897
         Lepidochitona.cinerea Loripes.orbiculatus Lucinella.divaricata
LR value                 2.773              31.348                6.172
Pr(>LR)                  0.981               0.001                0.830
         Magelona.papillicornis Maldane.glebifex Melinna.palmata
LR value                  2.773            2.773          26.860
Pr(>LR)                   0.981            0.981           0.002
         Microdeutopus.gryllotalpa Micromaldane.ornithochaeta Micronephthys.stammeri
LR value                    16.350                      6.655                  4.159
Pr(>LR)                      0.076                      0.812                  0.961
         Microphthalmus.fragilis Microphthalmus.sp. Monocorophium.acherusicum
LR value                   2.931             11.855                    39.891
Pr(>LR)                    0.981              0.306                     0.001
         Mytilaster.lineatus Mytilus.galloprovincialis Nemertea Nephtys.cirrosa
LR value              47.863                     2.773   10.046           2.773
Pr(>LR)                0.001                     0.981    0.484           0.981
         Nephtys.kersivalensis Nereis.perivisceralis Nereis.pulsatoria
LR value                 2.773                 2.773             6.238
Pr(>LR)                  0.981                 0.981             0.823
         Nototropis.guttatus Oligochaeta Paradoneis.harpagonea Parthenina.interstincta
LR value               7.210      36.765                 2.773                   4.546
Pr(>LR)                0.781       0.001                 0.981                   0.951
         Parvicardium.exiguum Perinereis.cultrifera Perioculodes.longimanus Phoronida
LR value                2.973                 6.689                   4.365     5.483
Pr(>LR)                 0.981                 0.812                   0.961     0.906
         Phyllodoce.sp. Platyhelminthes Platynereis.dumerilii Polititapes.aureus
LR value          4.159           8.508                 8.910             10.998
Pr(>LR)           0.961           0.642                 0.597              0.372
         Polychaeta.larvae Polydora.ciliata Polygordius.neapolitanus
LR value             4.159           41.905                    4.159
Pr(>LR)              0.961            0.001                    0.961
         Prionospio.cirrifera Protodorvillea.kefersteini Pseudocuma.longicorne
LR value               46.273                     30.140                 3.112
Pr(>LR)                 0.001                      0.001                 0.981
         Rissoa.membranacea Rissoa.splendida Salvatoria.clavata Schistomeringos.rudolphi
LR value              2.720           17.118             32.959                   13.822
Pr(>LR)               0.981            0.053              0.001                    0.172
         Sphaerosyllis.hystrix Spio.filicornis Spisula.subtruncata Stenosoma.capito
LR value                16.760          34.879               5.885           13.850
Pr(>LR)                  0.068           0.001               0.863            0.172
         Syllis.gracilis Syllis.hyalina Tellina.tenuis Thracia.phaseolina
LR value          28.543          4.555          4.499              2.773
Pr(>LR)            0.001          0.951          0.951              0.981
         Tricolia.pullus Tritia.neritea Tritia.reticulata Turbellaria Upogebia.pusilla
LR value          14.668          5.516            11.233       2.652           10.026
Pr(>LR)            0.118          0.903             0.353       0.981            0.484
Arguments:
 Test statistics calculated assuming response assumed to be uncorrelated 
 P-value calculated using 999 resampling iterations via pit.trap resampling (to account for correlation in testing).

The factor is highly significant according to the models.

Again, save the summary for safekeeping, but also run an anova.

write_rds(glms.lvm.zostera.2.summary, 
          here(save.dir, "glms_lvm_zostera_2_summary.RDS"))

Run the anova on the model.

(glms.lvm.zostera.2.aov <- anova.manyglm(glms.lvm.zostera.2, 
                                         test = "LR", p.uni = "adjusted", 
                                         nBoot = 999, ## limit the number of permutations for a shorter run time   
                                         show.time = "all") 
)
Resampling begins for test 1.
    Resampling run 0 finished. Time elapsed: 0.00 minutes...
    Resampling run 100 finished. Time elapsed: 0.12 minutes...
    Resampling run 200 finished. Time elapsed: 0.24 minutes...
    Resampling run 300 finished. Time elapsed: 0.36 minutes...
    Resampling run 400 finished. Time elapsed: 0.47 minutes...
    Resampling run 500 finished. Time elapsed: 0.59 minutes...
    Resampling run 600 finished. Time elapsed: 0.71 minutes...
    Resampling run 700 finished. Time elapsed: 0.83 minutes...
    Resampling run 800 finished. Time elapsed: 0.96 minutes...
    Resampling run 900 finished. Time elapsed: 1.09 minutes...
Time elapsed: 0 hr 1 min 12 sec
Analysis of Deviance Table

Model: manyglm(formula = zoo.mvabnd.zostera ~ lvm.clusters.zostera.2, 
Model:     family = "negative.binomial")

Multivariate test:
                       Res.Df Df.diff  Dev Pr(>Dev)    
(Intercept)                31                          
lvm.clusters.zostera.2     27       4 1223    0.001 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Univariate Tests:
                       Abra.alba          Abra.sp.          Actiniaria         
                             Dev Pr(>Dev)      Dev Pr(>Dev)        Dev Pr(>Dev)
(Intercept)                                                                    
lvm.clusters.zostera.2    27.461    0.003    4.159    1.000      2.773    1.000
                       Alitta.succinea          Ampelisca.diadema         
                                   Dev Pr(>Dev)               Dev Pr(>Dev)
(Intercept)                                                               
lvm.clusters.zostera.2          36.585    0.001             30.57    0.001
                       Amphibalanus.improvisus          Ampithoe.sp.         
                                           Dev Pr(>Dev)          Dev Pr(>Dev)
(Intercept)                                                                  
lvm.clusters.zostera.2                  23.408    0.009       12.209    0.430
                       Anadara.kagoshimensis          Apherusa.bispinosa         
                                         Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                                      
lvm.clusters.zostera.2                 2.773    1.000              2.773    1.000
                       Apseudopsis.ostroumovi          Bittium.reticulatum         
                                          Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                                                                        
lvm.clusters.zostera.2                 52.794    0.001              34.193    0.001
                       Brachynotus.sexdentatus          Capitella.capitata         
                                           Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                                        
lvm.clusters.zostera.2                   2.773    1.000             33.199    0.001
                       Capitella.minima          Chamelea.gallina         
                                    Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                               
lvm.clusters.zostera.2            7.227    0.944           28.525    0.002
                       Chironomidae.larvae          Cumella.limicola         
                                       Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                  
lvm.clusters.zostera.2               9.651    0.743           41.328    0.001
                       Cumella.pygmaea          Cytharella.costulata         
                                   Dev Pr(>Dev)                  Dev Pr(>Dev)
(Intercept)                                                                  
lvm.clusters.zostera.2           6.118    0.976                7.354    0.936
                       Diogenes.pugilator          Eteone.flava          Eunice.vittata
                                      Dev Pr(>Dev)          Dev Pr(>Dev)            Dev
(Intercept)                                                                            
lvm.clusters.zostera.2              3.059    1.000        4.159    1.000          3.779
                                Eurydice.dollfusi          Exogone.naidina         
                       Pr(>Dev)               Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                                        
lvm.clusters.zostera.2    1.000             6.118    0.976           8.477    0.887
                       Gastrosaccus.sanctus          Genetyllis.tuberculata         
                                        Dev Pr(>Dev)                    Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.2                2.773    1.000                  7.712    0.927
                       Glycera.sp.          Glycera.tridactyla         
                               Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                            
lvm.clusters.zostera.2       7.992    0.921              5.516    0.996
                       Glycera.unicornis          Harmothoe.imbricata         
                                     Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                                                                   
lvm.clusters.zostera.2             2.773    1.000               8.753    0.855
                       Harmothoe.reticulata          Heteromastus.filiformis         
                                        Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                                                                          
lvm.clusters.zostera.2                15.21    0.185                  28.142    0.002
                       Hirudinea          Hydrobia.acuta          Hydrobia.sp.         
                             Dev Pr(>Dev)            Dev Pr(>Dev)          Dev Pr(>Dev)
(Intercept)                                                                            
lvm.clusters.zostera.2     1.726    1.000          2.932    1.000        5.959    0.981
                       Iphinoe.tenella          Kellia.suborbicularis         
                                   Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                                   
lvm.clusters.zostera.2           9.824    0.727                 9.077    0.837
                       Lagis.koreni          Leiochone.leiopygos         
                                Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                                                              
lvm.clusters.zostera.2       16.471    0.135              15.331    0.183
                       Lentidium.mediterraneum          Lepidochitona.cinerea         
                                           Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                                           
lvm.clusters.zostera.2                   5.545    0.993                 2.773    1.000
                       Loripes.orbiculatus          Lucinella.divaricata         
                                       Dev Pr(>Dev)                  Dev Pr(>Dev)
(Intercept)                                                                      
lvm.clusters.zostera.2              31.348    0.001                6.172    0.976
                       Magelona.papillicornis          Maldane.glebifex         
                                          Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                     
lvm.clusters.zostera.2                  2.773    1.000            2.773    1.000
                       Melinna.palmata          Microdeutopus.gryllotalpa         
                                   Dev Pr(>Dev)                       Dev Pr(>Dev)
(Intercept)                                                                       
lvm.clusters.zostera.2           26.86    0.003                     16.35    0.135
                       Micromaldane.ornithochaeta          Micronephthys.stammeri
                                              Dev Pr(>Dev)                    Dev
(Intercept)                                                                      
lvm.clusters.zostera.2                      6.655    0.964                  4.159
                                Microphthalmus.fragilis          Microphthalmus.sp.
                       Pr(>Dev)                     Dev Pr(>Dev)                Dev
(Intercept)                                                                        
lvm.clusters.zostera.2    1.000                   2.931    1.000             11.855
                                Monocorophium.acherusicum          Mytilaster.lineatus
                       Pr(>Dev)                       Dev Pr(>Dev)                 Dev
(Intercept)                                                                           
lvm.clusters.zostera.2    0.463                    39.891    0.001              47.863
                                Mytilus.galloprovincialis          Nemertea         
                       Pr(>Dev)                       Dev Pr(>Dev)      Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.2    0.001                     2.773    1.000   10.046    0.715
                       Nephtys.cirrosa          Nephtys.kersivalensis         
                                   Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                                   
lvm.clusters.zostera.2           2.773    1.000                 2.773    1.000
                       Nereis.perivisceralis          Nereis.pulsatoria         
                                         Dev Pr(>Dev)               Dev Pr(>Dev)
(Intercept)                                                                     
lvm.clusters.zostera.2                 2.773    1.000             6.238    0.973
                       Nototropis.guttatus          Oligochaeta         
                                       Dev Pr(>Dev)         Dev Pr(>Dev)
(Intercept)                                                             
lvm.clusters.zostera.2                7.21    0.944      36.765    0.001
                       Paradoneis.harpagonea          Parthenina.interstincta         
                                         Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                                                                           
lvm.clusters.zostera.2                 2.773    1.000                   4.546    0.998
                       Parvicardium.exiguum          Perinereis.cultrifera         
                                        Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                                        
lvm.clusters.zostera.2                2.973    1.000                 6.689    0.964
                       Perioculodes.longimanus          Phoronida         
                                           Dev Pr(>Dev)       Dev Pr(>Dev)
(Intercept)                                                               
lvm.clusters.zostera.2                   4.365    0.999     5.483    0.996
                       Phyllodoce.sp.          Platyhelminthes         
                                  Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                            
lvm.clusters.zostera.2          4.159    1.000           8.508    0.887
                       Platynereis.dumerilii          Polititapes.aureus         
                                         Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                                      
lvm.clusters.zostera.2                  8.91    0.850             10.998    0.573
                       Polychaeta.larvae          Polydora.ciliata         
                                     Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                
lvm.clusters.zostera.2             4.159    1.000           41.905    0.001
                       Polygordius.neapolitanus          Prionospio.cirrifera         
                                            Dev Pr(>Dev)                  Dev Pr(>Dev)
(Intercept)                                                                           
lvm.clusters.zostera.2                    4.159    1.000               46.273    0.001
                       Protodorvillea.kefersteini          Pseudocuma.longicorne
                                              Dev Pr(>Dev)                   Dev
(Intercept)                                                                     
lvm.clusters.zostera.2                      30.14    0.002                 3.112
                                Rissoa.membranacea          Rissoa.splendida         
                       Pr(>Dev)                Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                          
lvm.clusters.zostera.2    1.000               2.72    1.000           17.118    0.115
                       Salvatoria.clavata          Schistomeringos.rudolphi         
                                      Dev Pr(>Dev)                      Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.2             32.959    0.001                   13.822    0.294
                       Sphaerosyllis.hystrix          Spio.filicornis         
                                         Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                                   
lvm.clusters.zostera.2                 16.76    0.128          34.879    0.001
                       Spisula.subtruncata          Stenosoma.capito         
                                       Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                  
lvm.clusters.zostera.2               5.885    0.981            13.85    0.294
                       Syllis.gracilis          Syllis.hyalina          Tellina.tenuis
                                   Dev Pr(>Dev)            Dev Pr(>Dev)            Dev
(Intercept)                                                                           
lvm.clusters.zostera.2          28.543    0.002          4.555    0.998          4.499
                                Thracia.phaseolina          Tricolia.pullus         
                       Pr(>Dev)                Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.2    0.998              2.773    1.000          14.668    0.221
                       Tritia.neritea          Tritia.reticulata          Turbellaria
                                  Dev Pr(>Dev)               Dev Pr(>Dev)         Dev
(Intercept)                                                                          
lvm.clusters.zostera.2          5.516    0.996            11.233    0.554       2.652
                                Upogebia.pusilla         
                       Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                              
lvm.clusters.zostera.2    1.000           10.026    0.715
Arguments:
 Test statistics calculated assuming uncorrelated response (for faster computation) 
P-value calculated using 999 resampling iterations via PIT-trap resampling (to account for correlation in testing.

Save the ANOVA, too.

write_rds(glms.lvm.zostera.2.aov, 
          here(save.dir, "glms_lvm_zostera_2_anova.RDS"))

NOW let’s get the taxa with the highest contributions to the tested pattern.

## get the top contributing species for the initial zostera GLMs 
(top.sp.glms.lvm.zostera.2 <- top_n_sp_glm(glms.lvm.zostera.2.aov, tot.dev.expl = 0.75)
)
[1] "Total deviance explained: 0.799"
    Apseudopsis.ostroumovi        Mytilaster.lineatus       Prionospio.cirrifera 
                 52.793744                  47.863335                  46.272692 
          Polydora.ciliata           Cumella.limicola  Monocorophium.acherusicum 
                 41.905219                  41.327723                  39.891356 
               Oligochaeta            Alitta.succinea            Spio.filicornis 
                 36.764590                  36.584687                  34.878811 
       Bittium.reticulatum         Capitella.capitata         Salvatoria.clavata 
                 34.192799                  33.198554                  32.958829 
       Loripes.orbiculatus          Ampelisca.diadema Protodorvillea.kefersteini 
                 31.347733                  30.569510                  30.139960 
           Syllis.gracilis           Chamelea.gallina    Heteromastus.filiformis 
                 28.542915                  28.524575                  28.142266 
                 Abra.alba            Melinna.palmata    Amphibalanus.improvisus 
                 27.461185                  26.859546                  23.408099 
          Rissoa.splendida      Sphaerosyllis.hystrix               Lagis.koreni 
                 17.117581                  16.760313                  16.471224 
 Microdeutopus.gryllotalpa        Leiochone.leiopygos       Harmothoe.reticulata 
                 16.349670                  15.331303                  15.209809 
           Tricolia.pullus           Stenosoma.capito   Schistomeringos.rudolphi 
                 14.667741                  13.849706                  13.822279 
              Ampithoe.sp.         Microphthalmus.sp.          Tritia.reticulata 
                 12.208710                  11.854688                  11.232600 
        Polititapes.aureus                   Nemertea           Upogebia.pusilla 
                 10.998455                  10.045834                  10.025894 
           Iphinoe.tenella        Chironomidae.larvae      Kellia.suborbicularis 
                  9.824385                   9.650905                   9.077281 
     Platynereis.dumerilii 
                  8.910425 
## unfortunately, mvabund likes to rename my species when converting the data to matrix (no spaces in names), and since I'm going to look them up in my initial untransformed count data, I have to change them back..   
names(top.sp.glms.lvm.zostera.2) <- names(top.sp.glms.lvm.zostera.2) %>% 
  str_replace(pattern = "\\.", replacement = " ")
top.sp.glms.lvm.zostera.2
    Apseudopsis ostroumovi        Mytilaster lineatus       Prionospio cirrifera 
                 52.793744                  47.863335                  46.272692 
          Polydora ciliata           Cumella limicola  Monocorophium acherusicum 
                 41.905219                  41.327723                  39.891356 
               Oligochaeta            Alitta succinea            Spio filicornis 
                 36.764590                  36.584687                  34.878811 
       Bittium reticulatum         Capitella capitata         Salvatoria clavata 
                 34.192799                  33.198554                  32.958829 
       Loripes orbiculatus          Ampelisca diadema Protodorvillea kefersteini 
                 31.347733                  30.569510                  30.139960 
           Syllis gracilis           Chamelea gallina    Heteromastus filiformis 
                 28.542915                  28.524575                  28.142266 
                 Abra alba            Melinna palmata    Amphibalanus improvisus 
                 27.461185                  26.859546                  23.408099 
          Rissoa splendida      Sphaerosyllis hystrix               Lagis koreni 
                 17.117581                  16.760313                  16.471224 
 Microdeutopus gryllotalpa        Leiochone leiopygos       Harmothoe reticulata 
                 16.349670                  15.331303                  15.209809 
           Tricolia pullus           Stenosoma capito   Schistomeringos rudolphi 
                 14.667741                  13.849706                  13.822279 
              Ampithoe sp.         Microphthalmus sp.          Tritia reticulata 
                 12.208710                  11.854688                  11.232600 
        Polititapes aureus                   Nemertea           Upogebia pusilla 
                 10.998455                  10.045834                  10.025894 
           Iphinoe tenella        Chironomidae larvae      Kellia suborbicularis 
                  9.824385                   9.650905                   9.077281 
     Platynereis dumerilii 
                  8.910425 

Try to plot these top contributing species - for whatever that’s worth, because 50 species on a plot is still a monstrosity.

## get the species and their abundances from the original count data, and transform them to long format
(abnd.top.sp.glms.lvm.zostera.2 <- zoo.abnd.zostera %>% 
   select(station, names(top.sp.glms.lvm.zostera.2)) %>% 
   gather(key = "species", value = "count", -station) %>% 
   ## turn species into a factor, or you'll be very very sorry later, when they're out of order on the plot. NB need to be in REVERSE order, because ggplot plots from bottom to top, and I want the top-contributing species on top. 
   mutate(species = factor(species, levels = rev(names(top.sp.glms.lvm.zostera.2))))
)
(plot.top.sp.glms.lvm.zostera.2 <- plot_top_n(abnd.top.sp.glms.lvm.zostera.2,
                                              mapping = aes(x = species, y = log_y_min(count), colour = station),
                                              labs.legend = paste0("Z", as.numeric(unique(abnd.top.sp.glms.lvm.zostera.2$station))),
                                              lab.y = "Abundance (log(y/min + 1))",
                                              palette = "Set2"
                                        ) +
    theme(legend.position = "top")
)

Extract the top-contributing species to each cluster (this same nightmare above, but as a table). This chunk is STILL hopelessly ugly and clumsy.

top.sp.abnd.glms.lvm.zostera.2 <- lapply(names(glms.lvm.zostera.2.summary$aliased), function(x) top_sp_glms_table(glms.lvm.zostera.2.summary, x, p = 0.05)) 
## fix species names (remove dot) 
top.sp.abnd.glms.lvm.zostera.2 <- lapply(top.sp.abnd.glms.lvm.zostera.2, function(x) x %>% mutate(species = str_replace(species, pattern = "\\.", replacement = " ")))
## rename columns (= group names) - right now they are something like "lvm.clusters.zostera2" etc.
top.sp.abnd.glms.lvm.zostera.2 <- lapply(top.sp.abnd.glms.lvm.zostera.2, function(x) x %>% rename_at(vars(contains("lvm.clusters.zostera.2")), list(~str_replace_all(., pattern = "lvm.clusters.zostera.2", "group_"))))
top.sp.abnd.glms.lvm.zostera.2 <- lapply(top.sp.abnd.glms.lvm.zostera.2, function(x) x %>% rename_at(vars(contains("Intercept")), list(~str_replace_all(., pattern = "\\(Intercept\\)", "group_1"))))
## pull the abundances from the original count df and add to the summary glm tables 
## make a long df of abundances & add clusters  
zoo.abnd.zostera.long.2 <- zoo.abnd.zostera %>%
  select(-c(month:replicate)) %>%
  gather(key = "species", value = "count", -station) %>% 
  mutate(group = case_when(station == "Poda" ~ 1,
                           station == "Otmanli" ~ 2, 
                           station == "Vromos" ~ 3, 
                           station == "Gradina" ~ 4, 
                           station == "Ropotamo" ~ 5)
         )
## sum sp abundances by group; nest by group
zoo.abnd.zostera.long.2.smry <- zoo.abnd.zostera.long.2 %>% 
  group_by(species, group) %>% 
  summarise(total_count = sum(count)) %>% 
  group_by(group) %>%
  nest()
## add the counts to the group dfs - wow that's an ugly, ugly hack. Wish I had more time to write this up properly.. 
top.sp.abnd.glms.lvm.zostera.2 <- map2(top.sp.abnd.glms.lvm.zostera.2, zoo.abnd.zostera.long.2.smry %>% pull(group), ~left_join(.x, zoo.abnd.zostera.long.2.smry %>% filter(group == .y) %>% unnest(), by = "species"))
## since these are sum counts over all the replicates (that's why the monstrous numbers), average them to be mean counts per group. NB different groups consist of different numbers of replicates, b.c. some groups consist of more than one station
(top.sp.abnd.glms.lvm.zostera.2 <- map2(top.sp.abnd.glms.lvm.zostera.2, c(8, 8, 4, 8, 4), function(x, y) x %>% mutate(mean_count = total_count/y))
)
[[1]]

[[2]]

[[3]]

[[4]]

[[5]]
NA

In the case of the seagrasses and case 2 clusters (= stations), the picture is still more unclear.. I suppose this is in no small part because of the differences 2013-14 - very marked for Poda and Otmanli. I suspect the stations changed in these two years (we were looking for Z. noltii in 2014 in particular) - but still, there is much variability. In the future, it’s probably going to be worth it to have more stations in a meadow, if we really want to have an idea of the communities there, and their variability.
The LRs seem to be a bit lower for groups 2, 4, maybe 5 too - still not sure if you can use that as a significance measure.
For now, in group 1 (= Z1), it’s hard to pick some characteristic species - because of the variability between 2013-2014, no doubt. The species/taxa with significantly higher abundance are: Bittium reticulatum, Capitella minima, Polydora ciliata, Prionosprio cirrifera (+ others, medium abundance); and the ones with a significantly lower abundance - or even absent - C. gallina, A. ostroumovi, S. clavata, C. limicola, C. costulata, S. hystrix, S. gracilis, T. pullus.
For group 2 (= Z2), the species with higher abundance - which is not really all that high; this group is also loose, hard to distinguish from group 1 - are: S. gracilis, M. lineatus, P. ciliata. The only species with lower abundance - in fact 0 - is Alitta succinea.
For group 3 (= Z3), the species with higher abundance are: M. acherusicum, S. filicornis, A. diadema. The species with lower abundance (or 0) are: B. reticulatum, P. ciliata, P. cirrifera, A. alba, A. succiena, S. clavata, Oligochaeta, A. improvisus.
For group 4 (= Z4), the species with higher abundance are: M. lineatus (very much so); C. limicola, P. kefersteini, C. gallina, C. capitata. The species with lower abundance (or 0) are: P. ciliata, P. cirrifera, A. succinea, A. improvisus, A. alba.
For group 5 (= Z5), the species with higher abundance are: A. ostroumovi, C. capitata, Oligochaeta. The species with lower abundance (or 0) are: R. splendida, T. pullus.

LVM clusters - case 3 Last try: group 1 = Z1-Z2, group 2 = Z3, group 3 = Z4, group 4 = Z5.
Check the model assumptions.

plot(manyglm(zoo.mvabnd.zostera ~ lvm.clusters.zostera.3, family = "negative.binomial"))

meanvar.plot(zoo.mvabnd.zostera ~ lvm.clusters.zostera.3, table = TRUE)
START SECTION 2 
Plotting if overlay is TRUE
using grouping variable lvm.clusters.zostera.3 160 mean values were 0 and could 
                                        not be included in the log-plot
using grouping variable lvm.clusters.zostera.3 160 variance values were 0 and could not 
                                        be included in the log-plot
FINISHED SECTION 2 
$mean
  Bittium.reticulatum Capitella.minima Oligochaeta Ampelisca.diadema Mytilaster.lineatus
1             57.6875          50.8125     30.0625              6.25               3.250
2              0.0000          88.0000      0.7500             80.50               2.250
3            238.3750          23.1250     48.6250             24.50              76.375
4             74.2500         124.0000    201.2500             20.25               2.750
  Heteromastus.filiformis Prionospio.cirrifera Polydora.ciliata
1                 17.8125               25.375          26.5625
2                  2.2500                0.000           0.0000
3                 23.0000                0.000           0.2500
4                  5.2500               20.000          11.2500
  Monocorophium.acherusicum Rissoa.membranacea Capitella.capitata Apseudopsis.ostroumovi
1                    3.9375             7.4375             0.4375                 0.0625
2                   78.2500             9.5000             0.0000                 0.0000
3                    1.0000            10.1250             9.8750                 3.8750
4                    2.2500             4.0000            39.7500                48.2500
  Spio.filicornis Microdeutopus.gryllotalpa Abra.alba Cumella.limicola
1          1.4375                     2.625    6.3125            0.375
2         38.2500                     4.250    0.0000            0.000
3          1.2500                     1.875    0.7500           10.250
4          0.0000                    14.000    1.7500            6.500
  Loripes.orbiculatus Parvicardium.exiguum Protodorvillea.kefersteini
1               1.125               2.8125                      0.750
2               0.500               5.5000                      0.000
3               8.750               2.8750                      9.875
4               4.500               1.5000                      1.250
  Platynereis.dumerilii Nemertea Syllis.gracilis Alitta.succinea Amphibalanus.improvisus
1                1.5625    2.375           1.625          3.5625                  3.3125
2                9.2500    0.500           0.000          0.0000                  0.2500
3                1.6250    3.125           0.875          0.0000                  0.2500
4                3.7500    1.500           7.250          1.0000                  0.5000
  Stenosoma.capito Lagis.koreni Schistomeringos.rudolphi Salvatoria.clavata
1            1.500        2.125                   1.6875              0.000
2            0.000        0.000                   0.0000              1.500
3            0.875        1.125                   1.2500              0.375
4            3.750        0.500                   0.0000              6.250
  Leiochone.leiopygos Melinna.palmata Microphthalmus.sp. Kellia.suborbicularis
1               0.625           0.875              0.000                0.3125
2               0.000           2.750              0.000                0.0000
3               1.875           0.000              0.625                2.3750
4               0.000           0.000              5.000                0.0000
  Nototropis.guttatus Chamelea.gallina Perinereis.cultrifera Sphaerosyllis.hystrix
1               0.750           0.0625                0.4375                0.1875
2               0.000           0.0000                0.0000                0.0000
3               0.125           2.0000                0.6250                1.3750
4               2.500           1.2500                2.0000                1.2500
  Ampithoe.sp. Harmothoe.reticulata Phoronida Perioculodes.longimanus Rissoa.splendida
1       0.1875                0.750    0.5625                   0.375             0.00
2       2.7500                0.000    0.0000                   1.250             1.00
3       0.5000                0.125    0.7500                   0.125             0.25
4       0.0000                1.000    0.2500                   0.750             2.25
  Diogenes.pugilator Iphinoe.tenella Platyhelminthes Exogone.naidina
1              0.375          0.6875          0.6875          0.0625
2              0.750          0.0000          0.0000          2.2500
3              0.250          0.2500          0.2500          0.2500
4              0.750          0.0000          0.0000          0.0000
  Genetyllis.tuberculata Parthenina.interstincta Tritia.reticulata Cytharella.costulata
1                  0.500                   0.625            0.5625               0.1875
2                  0.250                   0.000            0.0000               0.2500
3                  0.375                   0.250            0.2500               0.6250
4                  0.000                   0.000            0.2500               0.5000
  Syllis.hyalina Tricolia.pullus Turbellaria Harmothoe.imbricata Hydrobia.sp.
1            0.0          0.0625       0.375              0.3125        0.375
2            0.0          0.0000       0.250              0.0000        0.000
3            0.0          0.2500       0.375              0.2500        0.125
4            2.5          1.7500       0.000              0.0000        0.000
  Lucinella.divaricata Nereis.pulsatoria Polititapes.aureus Upogebia.pusilla Glycera.sp.
1                0.000            0.4375              0.375             0.00       0.375
2                0.000            0.0000              0.000             0.00       0.000
3                0.875            0.0000              0.125             0.00       0.000
4                0.000            0.0000              0.000             1.75       0.000
  Microphthalmus.fragilis Eunice.vittata Glycera.tridactyla Tritia.neritea
1                   0.375         0.1875             0.3125          0.250
2                   0.000         0.0000             0.0000          0.000
3                   0.000         0.0000             0.0000          0.125
4                   0.000         0.5000             0.0000          0.000
  Chironomidae.larvae Hydrobia.acuta Micromaldane.ornithochaeta Cumella.pygmaea
1                   0           0.25                      0.000           0.000
2                   0           0.00                      0.250           0.000
3                   0           0.00                      0.375           0.375
4                   1           0.00                      0.000           0.000
  Eurydice.dollfusi Hirudinea Pseudocuma.longicorne Spisula.subtruncata Tellina.tenuis
1             0.000     0.125                0.0625                0.00         0.0625
2             0.000     0.000                0.0000                0.00         0.0000
3             0.375     0.125                0.1250                0.25         0.2500
4             0.000     0.000                0.2500                0.25         0.0000
  Brachynotus.sexdentatus Lentidium.mediterraneum Micronephthys.stammeri Nephtys.cirrosa
1                  0.0625                    0.00                 0.0625          0.0625
2                  0.0000                    0.00                 0.0000          0.0000
3                  0.1250                    0.25                 0.0000          0.1250
4                  0.0000                    0.00                 0.2500          0.0000
  Abra.sp. Actiniaria Anadara.kagoshimensis Apherusa.bispinosa Eteone.flava
1     0.00     0.0625                0.0625              0.000         0.00
2     0.25     0.0000                0.0000              0.000         0.25
3     0.00     0.0000                0.0000              0.125         0.00
4     0.00     0.0000                0.0000              0.000         0.00
  Gastrosaccus.sanctus Glycera.unicornis Lepidochitona.cinerea Magelona.papillicornis
1                0.000            0.0625                 0.000                  0.000
2                0.000            0.0000                 0.000                  0.000
3                0.125            0.0000                 0.125                  0.125
4                0.000            0.0000                 0.000                  0.000
  Maldane.glebifex Mytilus.galloprovincialis Nephtys.kersivalensis Nereis.perivisceralis
1           0.0625                    0.0625                0.0625                 0.000
2           0.0000                    0.0000                0.0000                 0.000
3           0.0000                    0.0000                0.0000                 0.125
4           0.0000                    0.0000                0.0000                 0.000
  Paradoneis.harpagonea Phyllodoce.sp. Polychaeta.larvae Polygordius.neapolitanus
1                0.0625           0.00              0.00                     0.00
2                0.0000           0.25              0.25                     0.25
3                0.0000           0.00              0.00                     0.00
4                0.0000           0.00              0.00                     0.00
  Thracia.phaseolina
1              0.000
2              0.000
3              0.125
4              0.000

$var
  Bittium.reticulatum Capitella.minima Oligochaeta Ampelisca.diadema Mytilaster.lineatus
1            2642.229        2899.2292    700.8625          45.53333           35.000000
2               0.000        3094.0000      2.2500         395.00000            1.583333
3           25180.554         452.6964   3778.2679         735.14286          877.125000
4            3278.250        3103.3333  18570.9167          92.91667            2.916667
  Heteromastus.filiformis Prionospio.cirrifera Polydora.ciliata
1              177.495833             919.5833     1000.2625000
2                1.583333               0.0000        0.0000000
3              136.000000               0.0000        0.2142857
4               32.916667             183.3333       34.2500000
  Monocorophium.acherusicum Rissoa.membranacea Capitella.capitata Apseudopsis.ostroumovi
1                 17.929167         271.729167           1.595833               0.062500
2               3980.916667          11.666667           0.000000               0.000000
3                  1.428571          95.553571          82.982143               9.839286
4                  4.250000           6.666667         566.250000             196.250000
  Spio.filicornis Microdeutopus.gryllotalpa Abra.alba Cumella.limicola
1        2.529167                 10.783333 24.362500         1.183333
2      306.250000                 16.250000  0.000000         0.000000
3        3.357143                  2.696429  1.071429        30.500000
4        0.000000                 40.666667  1.583333        23.000000
  Loripes.orbiculatus Parvicardium.exiguum Protodorvillea.kefersteini
1            2.383333            18.829167                    2.60000
2            1.000000             3.666667                    0.00000
3           16.500000             8.410714                   16.69643
4            7.000000             1.666667                    2.25000
  Platynereis.dumerilii   Nemertea Syllis.gracilis Alitta.succinea
1              6.929167 12.2500000        7.450000      30.1291667
2             32.916667  0.3333333        0.000000       0.0000000
3              2.553571  3.8392857        2.982143       0.0000000
4             10.916667  3.6666667       22.916667       0.6666667
  Amphibalanus.improvisus Stenosoma.capito Lagis.koreni Schistomeringos.rudolphi
1              23.4291667       19.7333333    6.5166667                11.295833
2               0.2500000        0.0000000    0.0000000                 0.000000
3               0.2142857        0.9821429    0.9821429                 3.642857
4               1.0000000       12.9166667    0.3333333                 0.000000
  Salvatoria.clavata Leiochone.leiopygos Melinna.palmata Microphthalmus.sp.
1          0.0000000            0.650000        1.183333              0.000
2          0.3333333            0.000000        0.250000              0.000
3          1.1250000            3.839286        0.000000              3.125
4         14.9166667            0.000000        0.000000             22.000
  Kellia.suborbicularis Nototropis.guttatus Chamelea.gallina Perinereis.cultrifera
1             0.6291667            1.666667         0.062500             2.2625000
2             0.0000000            0.000000         0.000000             0.0000000
3            13.6964286            0.125000         1.714286             0.8392857
4             0.0000000           14.333333         1.583333             3.3333333
  Sphaerosyllis.hystrix Ampithoe.sp. Harmothoe.reticulata Phoronida
1             0.2958333    0.2958333            0.7333333 0.5291667
2             0.0000000   11.5833333            0.0000000 0.0000000
3             2.2678571    0.5714286            0.1250000 1.0714286
4             0.9166667    0.0000000            2.0000000 0.2500000
  Perioculodes.longimanus Rissoa.splendida Diogenes.pugilator Iphinoe.tenella
1               0.5166667        0.0000000          0.3833333        2.229167
2               3.5833333        2.0000000          0.2500000        0.000000
3               0.1250000        0.2142857          0.2142857        0.500000
4               0.9166667        6.9166667          0.9166667        0.000000
  Platyhelminthes Exogone.naidina Genetyllis.tuberculata Parthenina.interstincta
1       1.4291667          0.0625              2.2666667                    2.65
2       0.0000000          8.2500              0.2500000                    0.00
3       0.2142857          0.5000              0.5535714                    0.50
4       0.0000000          0.0000              0.0000000                    0.00
  Tritia.reticulata Cytharella.costulata Syllis.hyalina Tricolia.pullus Turbellaria
1         1.4625000            0.1625000              0       0.0625000       1.050
2         0.0000000            0.2500000              0       0.0000000       0.250
3         0.2142857            0.8392857              0       0.2142857       1.125
4         0.2500000            0.3333333             25       2.9166667       0.000
  Harmothoe.imbricata Hydrobia.sp. Lucinella.divaricata Nereis.pulsatoria
1           0.6291667     1.183333             0.000000            1.4625
2           0.0000000     0.000000             0.000000            0.0000
3           0.2142857     0.125000             3.267857            0.0000
4           0.0000000     0.000000             0.000000            0.0000
  Polititapes.aureus Upogebia.pusilla Glycera.sp. Microphthalmus.fragilis Eunice.vittata
1              0.650         0.000000   0.3833333                    2.25      0.2958333
2              0.000         0.000000   0.0000000                    0.00      0.0000000
3              0.125         0.000000   0.0000000                    0.00      0.0000000
4              0.000         5.583333   0.0000000                    0.00      1.0000000
  Glycera.tridactyla Tritia.neritea Chironomidae.larvae Hydrobia.acuta
1          0.6291667          0.600                   0              1
2          0.0000000          0.000                   0              0
3          0.0000000          0.125                   0              0
4          0.0000000          0.000                   2              0
  Micromaldane.ornithochaeta Cumella.pygmaea Eurydice.dollfusi Hirudinea
1                  0.0000000       0.0000000         0.0000000 0.1166667
2                  0.2500000       0.0000000         0.0000000 0.0000000
3                  0.5535714       0.5535714         0.5535714 0.1250000
4                  0.0000000       0.0000000         0.0000000 0.0000000
  Pseudocuma.longicorne Spisula.subtruncata Tellina.tenuis Brachynotus.sexdentatus
1                0.0625           0.0000000      0.0625000                  0.0625
2                0.0000           0.0000000      0.0000000                  0.0000
3                0.1250           0.2142857      0.2142857                  0.1250
4                0.2500           0.2500000      0.0000000                  0.0000
  Lentidium.mediterraneum Micronephthys.stammeri Nephtys.cirrosa Abra.sp. Actiniaria
1               0.0000000                 0.0625          0.0625     0.00     0.0625
2               0.0000000                 0.0000          0.0000     0.25     0.0000
3               0.2142857                 0.0000          0.1250     0.00     0.0000
4               0.0000000                 0.2500          0.0000     0.00     0.0000
  Anadara.kagoshimensis Apherusa.bispinosa Eteone.flava Gastrosaccus.sanctus
1                0.0625              0.000         0.00                0.000
2                0.0000              0.000         0.25                0.000
3                0.0000              0.125         0.00                0.125
4                0.0000              0.000         0.00                0.000
  Glycera.unicornis Lepidochitona.cinerea Magelona.papillicornis Maldane.glebifex
1            0.0625                 0.000                  0.000           0.0625
2            0.0000                 0.000                  0.000           0.0000
3            0.0000                 0.125                  0.125           0.0000
4            0.0000                 0.000                  0.000           0.0000
  Mytilus.galloprovincialis Nephtys.kersivalensis Nereis.perivisceralis
1                    0.0625                0.0625                 0.000
2                    0.0000                0.0000                 0.000
3                    0.0000                0.0000                 0.125
4                    0.0000                0.0000                 0.000
  Paradoneis.harpagonea Phyllodoce.sp. Polychaeta.larvae Polygordius.neapolitanus
1                0.0625           0.00              0.00                     0.00
2                0.0000           0.25              0.25                     0.25
3                0.0000           0.00              0.00                     0.00
4                0.0000           0.00              0.00                     0.00
  Thracia.phaseolina
1              0.000
2              0.000
3              0.125
4              0.000

More or less the same as case 2 before it.

  1. Assumed relationship between mean abundance and environmental variables - link function and formula.

Everything looks more or less fine; fit the model.

glms.lvm.zostera.3 <- manyglm(zoo.mvabnd.zostera ~ lvm.clusters.zostera.3, 
                              family = "negative.binomial")

Explore the fit (residuals, diagnostic plots, etc.).

## residuals vs fitted values
plot(glms.lvm.zostera.3)

## all traditional (g)lm diagnostic plots
plot.manyglm(glms.lvm.zostera.3, which = 1:3)

# ### source mvabund GLM plotting functions modified to use a grey palette - I just can't redo these plots on my own, the function is doing too complicated things internally to scale the x and y axes
# source(here(functions.dir, "default.plot.manyglm_grey.R"))
# source(here(functions.dir, "plot.manyglm_grey.R"))
# 
# par(mfrow = c(3,3))
# lapply(3:3, function(i) plot.manyglm.grey(glms.lvm.zostera, which = i, sub.caption = ""))
# par(mfrow = c(3, 3))

Save the model!

write_rds(glms.lvm.zostera.3, 
          here(save.dir, "glms_lvm_zostera_3.RDS"))

Let’s see the model summary (NB takes a LOT of time if there are many resamplings!).

(glms.lvm.zostera.3.summary <- summary(glms.lvm.zostera.3, 
                                       test = "LR", p.uni = "adjusted",
                                       nBoot = 999, ## limit the number of permutations if you just want to check it out
                                       show.time = "all")
)
    Resampling run 0 finished. Time elapsed: 0.00 min ...
    Resampling run 100 finished. Time elapsed: 0.36 min ...
    Resampling run 200 finished. Time elapsed: 0.72 min ...
    Resampling run 300 finished. Time elapsed: 1.07 min ...
    Resampling run 400 finished. Time elapsed: 1.43 min ...
    Resampling run 500 finished. Time elapsed: 1.78 min ...
    Resampling run 600 finished. Time elapsed: 2.14 min ...
    Resampling run 700 finished. Time elapsed: 2.50 min ...
    Resampling run 800 finished. Time elapsed: 2.86 min ...
    Resampling run 900 finished. Time elapsed: 3.21 min ...
Time elapsed: 0 hr 3 min 34 sec

Test statistics:
                        LR value Pr(>LR)    
(Intercept)               1394.5   0.001 ***
lvm.clusters.zostera.32    358.1   0.001 ***
lvm.clusters.zostera.33    423.5   0.001 ***
lvm.clusters.zostera.34    335.3   0.001 ***
--- 
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Univariate test statistic: 
                           (Intercept)         lvm.clusters.zostera.32        
                              LR value Pr(>LR)                LR value Pr(>LR)
Abra.alba                       47.727   0.001                  18.148   0.004
Abra.sp.                         6.107   0.547                   3.219   0.632
Actiniaria                       2.833   0.939                   0.446   0.990
Alitta.succinea                  8.284   0.276                   5.558   0.259
Ampelisca.diadema               45.273   0.001                  20.069   0.002
Amphibalanus.improvisus         15.404   0.025                   5.997   0.240
Ampithoe.sp.                     5.782   0.605                   6.490   0.224
Anadara.kagoshimensis            2.833   0.939                   0.446   0.990
Apherusa.bispinosa               5.024   0.728                   0.000   1.000
Apseudopsis.ostroumovi          21.836   0.019                   0.445   0.990
Bittium.reticulatum            159.822   0.001                  25.436   0.002
Brachynotus.sexdentatus          4.881   0.753                   0.446   0.990
Capitella.capitata               3.390   0.925                   2.606   0.762
Capitella.minima               158.885   0.001                   0.860   0.984
Chamelea.gallina                21.471   0.019                   0.446   0.990
Chironomidae.larvae              9.401   0.220                   0.000   0.996
Cumella.limicola                 6.366   0.532                   2.538   0.774
Cumella.pygmaea                  7.559   0.402                   0.000   1.000
Cytharella.costulata            10.276   0.177                   0.059   0.996
Diogenes.pugilator               7.671   0.396                   0.877   0.984
Eteone.flava                     6.107   0.547                   3.219   0.632
Eunice.vittata                   3.020   0.926                   1.027   0.968
Eurydice.dollfusi                7.559   0.402                   0.000   1.000
Exogone.naidina                  6.206   0.534                   5.880   0.240
Gastrosaccus.sanctus             5.024   0.728                   0.000   1.000
Genetyllis.tuberculata           0.996   0.986                   0.185   0.996
Glycera.sp.                      4.780   0.753                   2.664   0.745
Glycera.tridactyla               2.091   0.973                   1.471   0.930
Glycera.unicornis                2.833   0.939                   0.446   0.990
Harmothoe.imbricata              3.139   0.926                   1.743   0.883
Harmothoe.reticulata             0.997   0.986                   5.096   0.313
Heteromastus.filiformis        123.751   0.001                  11.936   0.030
Hirudinea                        5.835   0.594                   0.893   0.984
Hydrobia.acuta                   0.471   0.986                   0.467   0.989
Hydrobia.sp.                     0.941   0.986                   1.166   0.950
Iphinoe.tenella                  0.542   0.986                   2.867   0.704
Kellia.suborbicularis            2.897   0.939                   1.598   0.914
Lagis.koreni                     6.615   0.510                   8.571   0.108
Leiochone.leiopygos              1.958   0.977                   4.059   0.486
Lentidium.mediterraneum          9.353   0.224                   0.000   0.996
Lepidochitona.cinerea            5.024   0.728                   0.000   1.000
Loripes.orbiculatus              0.205   0.986                   1.283   0.950
Lucinella.divaricata             5.816   0.600                   0.000   1.000
Magelona.papillicornis           5.024   0.728                   0.000   1.000
Maldane.glebifex                 2.833   0.939                   0.446   0.990
Melinna.palmata                  0.261   0.986                   6.839   0.200
Microdeutopus.gryllotalpa       13.341   0.044                   0.870   0.984
Micromaldane.ornithochaeta       9.788   0.198                   3.053   0.656
Micronephthys.stammeri           5.710   0.605                   0.446   0.990
Microphthalmus.fragilis          0.234   0.986                   0.467   0.989
Microphthalmus.sp.               9.420   0.219                   0.000   1.000
Monocorophium.acherusicum       26.934   0.005                  26.810   0.001
Mytilaster.lineatus             17.441   0.019                   0.324   0.993
Mytilus.galloprovincialis        2.833   0.939                   0.446   0.990
Nemertea                         9.059   0.233                   3.320   0.631
Nephtys.cirrosa                  4.881   0.753                   0.446   0.990
Nephtys.kersivalensis            2.833   0.939                   0.446   0.990
Nereis.perivisceralis            5.024   0.728                   0.000   1.000
Nereis.pulsatoria                0.491   0.986                   0.980   0.971
Nototropis.guttatus              0.323   0.986                   2.976   0.669
Oligochaeta                    126.966   0.001                  15.119   0.007
Paradoneis.harpagonea            2.833   0.939                   0.446   0.990
Parthenina.interstincta          0.301   0.986                   1.536   0.924
Parvicardium.exiguum            14.018   0.039                   1.502   0.930
Perinereis.cultrifera            1.844   0.981                   2.060   0.867
Perioculodes.longimanus          3.981   0.870                   2.049   0.869
Phoronida                        3.161   0.926                   3.937   0.509
Phyllodoce.sp.                   6.107   0.547                   3.219   0.632
Platyhelminthes                  0.644   0.986                   3.118   0.642
Platynereis.dumerilii            1.824   0.981                   7.414   0.173
Polititapes.aureus               2.789   0.939                   2.081   0.863
Polychaeta.larvae                6.107   0.547                   3.219   0.632
Polydora.ciliata                81.609   0.001                  15.796   0.005
Polygordius.neapolitanus         6.107   0.547                   3.219   0.632
Prionospio.cirrifera            91.317   0.001                  19.403   0.002
Protodorvillea.kefersteini       0.820   0.986                   4.746   0.362
Pseudocuma.longicorne            7.101   0.453                   0.446   0.990
Rissoa.membranacea              50.503   0.001                   0.160   0.996
Rissoa.splendida                17.291   0.019                  10.624   0.047
Salvatoria.clavata              25.703   0.006                  18.216   0.004
Schistomeringos.rudolphi         0.703   0.986                   2.760   0.729
Sphaerosyllis.hystrix           10.217   0.179                   1.307   0.949
Spio.filicornis                  1.763   0.981                  24.367   0.002
Spisula.subtruncata             11.731   0.089                   0.000   1.000
Stenosoma.capito                 1.007   0.986                   4.916   0.344
Syllis.gracilis                  1.598   0.981                   5.347   0.283
Syllis.hyalina                   3.627   0.894                   0.000   0.996
Tellina.tenuis                   7.795   0.377                   0.446   0.990
Thracia.phaseolina               5.024   0.728                   0.000   1.000
Tricolia.pullus                 13.409   0.043                   0.445   0.990
Tritia.neritea                   1.950   0.978                   1.104   0.961
Tritia.reticulata                1.128   0.983                   2.531   0.777
Turbellaria                      1.449   0.981                   0.056   0.996
Upogebia.pusilla                 8.660   0.248                   0.000   1.000
                           lvm.clusters.zostera.33         lvm.clusters.zostera.34
                                          LR value Pr(>LR)                LR value
Abra.alba                                   15.271   0.010                   4.994
Abra.sp.                                     0.000   1.000                   0.000
Actiniaria                                   0.811   1.000                   0.446
Alitta.succinea                              9.839   0.093                   1.072
Ampelisca.diadema                            8.950   0.133                   4.744
Amphibalanus.improvisus                     10.321   0.082                   4.259
Ampithoe.sp.                                 1.064   1.000                   1.175
Anadara.kagoshimensis                        0.811   1.000                   0.446
Apherusa.bispinosa                           2.197   0.995                   0.000
Apseudopsis.ostroumovi                      32.536   0.001                  46.727
Bittium.reticulatum                         10.139   0.084                   0.217
Brachynotus.sexdentatus                      0.236   1.000                   0.446
Capitella.capitata                          18.553   0.002                  25.101
Capitella.minima                             2.320   0.991                   2.355
Chamelea.gallina                            22.820   0.002                  11.133
Chironomidae.larvae                          0.000   1.000                   7.676
Cumella.limicola                            27.637   0.001                  20.452
Cumella.pygmaea                              4.909   0.612                   0.000
Cytharella.costulata                         2.833   0.963                   1.046
Diogenes.pugilator                           0.263   1.000                   0.877
Eteone.flava                                 0.000   1.000                   0.000
Eunice.vittata                               1.873   0.999                   0.483
Eurydice.dollfusi                            4.909   0.612                   0.000
Exogone.naidina                              1.012   1.000                   0.416
Gastrosaccus.sanctus                         2.197   0.995                   0.000
Genetyllis.tuberculata                       0.063   1.000                   1.888
Glycera.sp.                                  4.773   0.632                   2.664
Glycera.tridactyla                           2.652   0.977                   1.471
Glycera.unicornis                            0.811   1.000                   0.446
Harmothoe.imbricata                          0.047   1.000                   1.743
Harmothoe.reticulata                         4.553   0.677                   0.222
Heteromastus.filiformis                      0.653   1.000                   5.770
Hirudinea                                    0.000   1.000                   0.893
Hydrobia.acuta                               0.845   1.000                   0.467
Hydrobia.sp.                                 0.396   1.000                   1.166
Iphinoe.tenella                              0.979   1.000                   2.867
Kellia.suborbicularis                        4.332   0.730                   1.598
Lagis.koreni                                 1.378   1.000                   2.889
Leiochone.leiopygos                          4.772   0.633                   4.059
Lentidium.mediterraneum                      4.394   0.718                   0.000
Lepidochitona.cinerea                        2.197   0.995                   0.000
Loripes.orbiculatus                         23.881   0.002                   9.848
Lucinella.divaricata                         4.958   0.603                   0.000
Magelona.papillicornis                       2.197   0.995                   0.000
Maldane.glebifex                             0.811   1.000                   0.446
Melinna.palmata                             11.353   0.053                   6.248
Microdeutopus.gryllotalpa                    0.549   1.000                  10.829
Micromaldane.ornithochaeta                   5.601   0.498                   0.000
Micronephthys.stammeri                       0.811   1.000                   0.893
Microphthalmus.fragilis                      0.845   1.000                   0.467
Microphthalmus.sp.                           6.434   0.390                  10.604
Monocorophium.acherusicum                    6.554   0.382                   0.880
Mytilaster.lineatus                         28.164   0.001                   0.072
Mytilus.galloprovincialis                    0.811   1.000                   0.446
Nemertea                                     0.344   1.000                   0.460
Nephtys.cirrosa                              0.236   1.000                   0.446
Nephtys.kersivalensis                        0.811   1.000                   0.446
Nereis.perivisceralis                        2.197   0.995                   0.000
Nereis.pulsatoria                            1.766   0.999                   0.980
Nototropis.guttatus                          2.256   0.995                   1.529
Oligochaeta                                  1.311   1.000                  12.946
Paradoneis.harpagonea                        0.811   1.000                   0.446
Parthenina.interstincta                      0.348   1.000                   1.536
Parvicardium.exiguum                         0.002   1.000                   0.885
Perinereis.cultrifera                        0.146   1.000                   2.073
Perioculodes.longimanus                      1.060   1.000                   0.584
Phoronida                                    0.286   1.000                   0.722
Phyllodoce.sp.                               0.000   1.000                   0.000
Platyhelminthes                              1.116   1.000                   3.118
Platynereis.dumerilii                        0.005   1.000                   1.755
Polititapes.aureus                           0.920   1.000                   2.081
Polychaeta.larvae                            0.000   1.000                   0.000
Polydora.ciliata                            20.565   0.002                   1.275
Polygordius.neapolitanus                     0.000   1.000                   0.000
Prionospio.cirrifera                        31.954   0.001                   0.160
Protodorvillea.kefersteini                  18.752   0.002                   0.636
Pseudocuma.longicorne                        0.236   1.000                   0.893
Rissoa.membranacea                           0.416   1.000                   0.818
Rissoa.splendida                             4.195   0.748                  16.268
Salvatoria.clavata                           6.518   0.382                  31.870
Schistomeringos.rudolphi                     0.066   1.000                   2.760
Sphaerosyllis.hystrix                        8.440   0.170                   5.462
Spio.filicornis                              0.088   1.000                   7.758
Spisula.subtruncata                          4.394   0.719                   3.219
Stenosoma.capito                             0.492   1.000                   1.211
Syllis.gracilis                              0.703   1.000                   3.662
Syllis.hyalina                               0.000   1.000                   3.584
Tellina.tenuis                               1.386   1.000                   0.446
Thracia.phaseolina                           2.197   0.995                   0.000
Tricolia.pullus                              1.365   1.000                  11.315
Tritia.neritea                               0.205   1.000                   1.104
Tritia.reticulata                            0.624   1.000                   0.361
Turbellaria                                  0.000   1.000                   1.475
Upogebia.pusilla                             0.000   1.000                   8.030
                                  
                           Pr(>LR)
Abra.alba                    0.596
Abra.sp.                     1.000
Actiniaria                   1.000
Alitta.succinea              1.000
Ampelisca.diadema            0.632
Amphibalanus.improvisus      0.702
Ampithoe.sp.                 1.000
Anadara.kagoshimensis        1.000
Apherusa.bispinosa           1.000
Apseudopsis.ostroumovi       0.001
Bittium.reticulatum          1.000
Brachynotus.sexdentatus      1.000
Capitella.capitata           0.001
Capitella.minima             0.965
Chamelea.gallina             0.068
Chironomidae.larvae          0.237
Cumella.limicola             0.001
Cumella.pygmaea              1.000
Cytharella.costulata         1.000
Diogenes.pugilator           1.000
Eteone.flava                 1.000
Eunice.vittata               1.000
Eurydice.dollfusi            1.000
Exogone.naidina              1.000
Gastrosaccus.sanctus         1.000
Genetyllis.tuberculata       0.988
Glycera.sp.                  0.944
Glycera.tridactyla           0.997
Glycera.unicornis            1.000
Harmothoe.imbricata          0.991
Harmothoe.reticulata         1.000
Heteromastus.filiformis      0.459
Hirudinea                    1.000
Hydrobia.acuta               1.000
Hydrobia.sp.                 1.000
Iphinoe.tenella              0.903
Kellia.suborbicularis        0.995
Lagis.koreni                 0.903
Leiochone.leiopygos          0.735
Lentidium.mediterraneum      1.000
Lepidochitona.cinerea        1.000
Loripes.orbiculatus          0.104
Lucinella.divaricata         1.000
Magelona.papillicornis       1.000
Maldane.glebifex             1.000
Melinna.palmata              0.399
Microdeutopus.gryllotalpa    0.075
Micromaldane.ornithochaeta   1.000
Micronephthys.stammeri       1.000
Microphthalmus.fragilis      1.000
Microphthalmus.sp.           0.079
Monocorophium.acherusicum    1.000
Mytilaster.lineatus          1.000
Mytilus.galloprovincialis    1.000
Nemertea                     1.000
Nephtys.cirrosa              1.000
Nephtys.kersivalensis        1.000
Nereis.perivisceralis        1.000
Nereis.pulsatoria            1.000
Nototropis.guttatus          0.996
Oligochaeta                  0.027
Paradoneis.harpagonea        1.000
Parthenina.interstincta      0.996
Parvicardium.exiguum         1.000
Perinereis.cultrifera        0.980
Perioculodes.longimanus      1.000
Phoronida                    1.000
Phyllodoce.sp.               1.000
Platyhelminthes              0.867
Platynereis.dumerilii        0.991
Polititapes.aureus           0.979
Polychaeta.larvae            1.000
Polydora.ciliata             1.000
Polygordius.neapolitanus     1.000
Prionospio.cirrifera         1.000
Protodorvillea.kefersteini   1.000
Pseudocuma.longicorne        1.000
Rissoa.membranacea           1.000
Rissoa.splendida             0.005
Salvatoria.clavata           0.001
Schistomeringos.rudolphi     0.926
Sphaerosyllis.hystrix        0.498
Spio.filicornis              0.233
Spisula.subtruncata          0.854
Stenosoma.capito             1.000
Syllis.gracilis              0.797
Syllis.hyalina               0.797
Tellina.tenuis               1.000
Thracia.phaseolina           1.000
Tricolia.pullus              0.060
Tritia.neritea               1.000
Tritia.reticulata            1.000
Turbellaria                  0.997
Upogebia.pusilla             0.216

Arguments: with 999 resampling iterations using pit.trap resampling and response assumed to be uncorrelated 

Likelihood Ratio statistic:  965.7, p-value: 0.001 

Univariate test statistic: 
         Abra.alba Abra.sp. Actiniaria Alitta.succinea Ampelisca.diadema
LR value    27.438    4.159      1.386          13.528            20.153
Pr(>LR)      0.002    0.933      0.994           0.119             0.010
         Amphibalanus.improvisus Ampithoe.sp. Anadara.kagoshimensis Apherusa.bispinosa
LR value                  15.231        8.727                 1.386              2.773
Pr(>LR)                    0.076        0.517                 0.994              0.983
         Apseudopsis.ostroumovi Bittium.reticulatum Brachynotus.sexdentatus
LR value                 51.414              34.189                   1.386
Pr(>LR)                   0.001               0.001                   0.994
         Capitella.capitata Capitella.minima Chamelea.gallina Chironomidae.larvae
LR value             30.336            6.793           27.138               9.651
Pr(>LR)               0.002            0.718            0.002               0.396
         Cumella.limicola Cumella.pygmaea Cytharella.costulata Diogenes.pugilator
LR value           33.634           6.118                3.195              2.380
Pr(>LR)             0.001           0.804                0.983              0.991
         Eteone.flava Eunice.vittata Eurydice.dollfusi Exogone.naidina
LR value        4.159          3.572             6.118           7.227
Pr(>LR)         0.933          0.977             0.804           0.690
         Gastrosaccus.sanctus Genetyllis.tuberculata Glycera.sp. Glycera.tridactyla
LR value                2.773                  1.966       7.992              4.484
Pr(>LR)                 0.983                  0.994       0.575              0.925
         Glycera.unicornis Harmothoe.imbricata Harmothoe.reticulata
LR value             1.386               3.192                9.416
Pr(>LR)              0.994               0.983                0.421
         Heteromastus.filiformis Hirudinea Hydrobia.acuta Hydrobia.sp. Iphinoe.tenella
LR value                  17.463     1.726          1.438        2.250           5.470
Pr(>LR)                    0.027     0.994          0.994        0.991           0.869
         Kellia.suborbicularis Lagis.koreni Leiochone.leiopygos Lentidium.mediterraneum
LR value                 8.973       10.472              14.995                   5.545
Pr(>LR)                  0.469        0.312               0.077                   0.865
         Lepidochitona.cinerea Loripes.orbiculatus Lucinella.divaricata
LR value                 2.773              28.176                6.172
Pr(>LR)                  0.983               0.002                0.795
         Magelona.papillicornis Maldane.glebifex Melinna.palmata
LR value                  2.773            1.386          24.203
Pr(>LR)                   0.983            0.994           0.003
         Microdeutopus.gryllotalpa Micromaldane.ornithochaeta Micronephthys.stammeri
LR value                    13.747                      6.655                  2.773
Pr(>LR)                      0.113                      0.721                  0.983
         Microphthalmus.fragilis Microphthalmus.sp. Monocorophium.acherusicum
LR value                   1.437             11.855                    39.678
Pr(>LR)                    0.994              0.208                     0.001
         Mytilaster.lineatus Mytilus.galloprovincialis Nemertea Nephtys.cirrosa
LR value              34.910                     1.386    4.566           1.386
Pr(>LR)                0.001                     0.994    0.925           0.994
         Nephtys.kersivalensis Nereis.perivisceralis Nereis.pulsatoria
LR value                 1.386                 2.773             2.987
Pr(>LR)                  0.994                 0.983             0.983
         Nototropis.guttatus Oligochaeta Paradoneis.harpagonea Parthenina.interstincta
LR value               7.095      27.378                 1.386                   2.884
Pr(>LR)                0.690       0.002                 0.994                   0.983
         Parvicardium.exiguum Perinereis.cultrifera Perioculodes.longimanus Phoronida
LR value                2.911                 4.654                   4.365     5.372
Pr(>LR)                 0.983                 0.925                   0.925     0.879
         Phyllodoce.sp. Platyhelminthes Platynereis.dumerilii Polititapes.aureus
LR value          4.159           5.906                 8.537              4.065
Pr(>LR)           0.933           0.834                 0.523              0.943
         Polychaeta.larvae Polydora.ciliata Polygordius.neapolitanus
LR value             4.159           29.489                    4.159
Pr(>LR)              0.933            0.002                    0.933
         Prionospio.cirrifera Protodorvillea.kefersteini Pseudocuma.longicorne
LR value               41.351                     25.261                 1.726
Pr(>LR)                 0.001                      0.002                 0.994
         Rissoa.membranacea Rissoa.splendida Salvatoria.clavata Schistomeringos.rudolphi
LR value              1.701           17.118             32.959                    5.024
Pr(>LR)               0.994            0.032              0.001                    0.900
         Sphaerosyllis.hystrix Spio.filicornis Spisula.subtruncata Stenosoma.capito
LR value                12.736          34.632               5.885            7.189
Pr(>LR)                  0.154           0.001               0.834            0.690
         Syllis.gracilis Syllis.hyalina Tellina.tenuis Thracia.phaseolina
LR value          10.712          4.555          3.112              2.773
Pr(>LR)            0.306          0.925          0.983              0.983
         Tricolia.pullus Tritia.neritea Tritia.reticulata Turbellaria Upogebia.pusilla
LR value          13.288          2.037             2.932       1.527           10.026
Pr(>LR)            0.128          0.994             0.983       0.994            0.353
Arguments:
 Test statistics calculated assuming response assumed to be uncorrelated 
 P-value calculated using 999 resampling iterations via pit.trap resampling (to account for correlation in testing).

The factor is highly significant according to the models.

Again, save the summary for safekeeping, but also run an anova.

write_rds(glms.lvm.zostera.3.summary, 
          here(save.dir, "glms_lvm_zostera_3_summary.RDS"))

Run the anova on the model.

(glms.lvm.zostera.3.aov <- anova.manyglm(glms.lvm.zostera.3, 
                                         test = "LR", p.uni = "adjusted", 
                                         nBoot = 999, ## limit the number of permutations for a shorter run time   
                                         show.time = "all") 
)
Resampling begins for test 1.
    Resampling run 0 finished. Time elapsed: 0.00 minutes...
    Resampling run 100 finished. Time elapsed: 0.12 minutes...
    Resampling run 200 finished. Time elapsed: 0.24 minutes...
    Resampling run 300 finished. Time elapsed: 0.36 minutes...
    Resampling run 400 finished. Time elapsed: 0.48 minutes...
    Resampling run 500 finished. Time elapsed: 0.59 minutes...
    Resampling run 600 finished. Time elapsed: 0.71 minutes...
    Resampling run 700 finished. Time elapsed: 0.83 minutes...
    Resampling run 800 finished. Time elapsed: 0.95 minutes...
    Resampling run 900 finished. Time elapsed: 1.08 minutes...
Time elapsed: 0 hr 1 min 11 sec
Analysis of Deviance Table

Model: manyglm(formula = zoo.mvabnd.zostera ~ lvm.clusters.zostera.3, 
Model:     family = "negative.binomial")

Multivariate test:
                       Res.Df Df.diff   Dev Pr(>Dev)    
(Intercept)                31                           
lvm.clusters.zostera.3     28       3 965.7    0.001 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Univariate Tests:
                       Abra.alba          Abra.sp.          Actiniaria         
                             Dev Pr(>Dev)      Dev Pr(>Dev)        Dev Pr(>Dev)
(Intercept)                                                                    
lvm.clusters.zostera.3    27.438    0.004    4.159    1.000      1.386    1.000
                       Alitta.succinea          Ampelisca.diadema         
                                   Dev Pr(>Dev)               Dev Pr(>Dev)
(Intercept)                                                               
lvm.clusters.zostera.3          13.528    0.176            20.153    0.018
                       Amphibalanus.improvisus          Ampithoe.sp.         
                                           Dev Pr(>Dev)          Dev Pr(>Dev)
(Intercept)                                                                  
lvm.clusters.zostera.3                  15.231    0.106        8.727    0.672
                       Anadara.kagoshimensis          Apherusa.bispinosa         
                                         Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                                      
lvm.clusters.zostera.3                 1.386    1.000              2.773    1.000
                       Apseudopsis.ostroumovi          Bittium.reticulatum         
                                          Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                                                                        
lvm.clusters.zostera.3                 51.414    0.001              34.189    0.002
                       Brachynotus.sexdentatus          Capitella.capitata         
                                           Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                                        
lvm.clusters.zostera.3                   1.386    1.000             30.336    0.002
                       Capitella.minima          Chamelea.gallina         
                                    Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                               
lvm.clusters.zostera.3            6.793    0.895           27.138    0.004
                       Chironomidae.larvae          Cumella.limicola         
                                       Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                  
lvm.clusters.zostera.3               9.651    0.562           33.634    0.002
                       Cumella.pygmaea          Cytharella.costulata         
                                   Dev Pr(>Dev)                  Dev Pr(>Dev)
(Intercept)                                                                  
lvm.clusters.zostera.3           6.118    0.944                3.195    1.000
                       Diogenes.pugilator          Eteone.flava          Eunice.vittata
                                      Dev Pr(>Dev)          Dev Pr(>Dev)            Dev
(Intercept)                                                                            
lvm.clusters.zostera.3               2.38    1.000        4.159    1.000          3.572
                                Eurydice.dollfusi          Exogone.naidina         
                       Pr(>Dev)               Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                                        
lvm.clusters.zostera.3    1.000             6.118    0.944           7.227    0.875
                       Gastrosaccus.sanctus          Genetyllis.tuberculata         
                                        Dev Pr(>Dev)                    Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.3                2.773    1.000                  1.966    1.000
                       Glycera.sp.          Glycera.tridactyla         
                               Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                            
lvm.clusters.zostera.3       7.992    0.788              4.484    0.993
                       Glycera.unicornis          Harmothoe.imbricata         
                                     Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                                                                   
lvm.clusters.zostera.3             1.386    1.000               3.192    1.000
                       Harmothoe.reticulata          Heteromastus.filiformis         
                                        Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                                                                          
lvm.clusters.zostera.3                9.416    0.602                  17.463    0.050
                       Hirudinea          Hydrobia.acuta          Hydrobia.sp.         
                             Dev Pr(>Dev)            Dev Pr(>Dev)          Dev Pr(>Dev)
(Intercept)                                                                            
lvm.clusters.zostera.3     1.726    1.000          1.438    1.000         2.25    1.000
                       Iphinoe.tenella          Kellia.suborbicularis         
                                   Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                                   
lvm.clusters.zostera.3            5.47    0.983                 8.973    0.652
                       Lagis.koreni          Leiochone.leiopygos         
                                Dev Pr(>Dev)                 Dev Pr(>Dev)
(Intercept)                                                              
lvm.clusters.zostera.3       10.472    0.437              14.995    0.108
                       Lentidium.mediterraneum          Lepidochitona.cinerea         
                                           Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                                           
lvm.clusters.zostera.3                   5.545    0.981                 2.773    1.000
                       Loripes.orbiculatus          Lucinella.divaricata         
                                       Dev Pr(>Dev)                  Dev Pr(>Dev)
(Intercept)                                                                      
lvm.clusters.zostera.3              28.176    0.004                6.172    0.942
                       Magelona.papillicornis          Maldane.glebifex         
                                          Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                     
lvm.clusters.zostera.3                  2.773    1.000            1.386    1.000
                       Melinna.palmata          Microdeutopus.gryllotalpa         
                                   Dev Pr(>Dev)                       Dev Pr(>Dev)
(Intercept)                                                                       
lvm.clusters.zostera.3          24.203    0.004                    13.747    0.172
                       Micromaldane.ornithochaeta          Micronephthys.stammeri
                                              Dev Pr(>Dev)                    Dev
(Intercept)                                                                      
lvm.clusters.zostera.3                      6.655    0.908                  2.773
                                Microphthalmus.fragilis          Microphthalmus.sp.
                       Pr(>Dev)                     Dev Pr(>Dev)                Dev
(Intercept)                                                                        
lvm.clusters.zostera.3    1.000                   1.437    1.000             11.855
                                Monocorophium.acherusicum          Mytilaster.lineatus
                       Pr(>Dev)                       Dev Pr(>Dev)                 Dev
(Intercept)                                                                           
lvm.clusters.zostera.3    0.278                    39.678    0.001               34.91
                                Mytilus.galloprovincialis          Nemertea         
                       Pr(>Dev)                       Dev Pr(>Dev)      Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.3    0.002                     1.386    1.000    4.566    0.991
                       Nephtys.cirrosa          Nephtys.kersivalensis         
                                   Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                                   
lvm.clusters.zostera.3           1.386    1.000                 1.386    1.000
                       Nereis.perivisceralis          Nereis.pulsatoria         
                                         Dev Pr(>Dev)               Dev Pr(>Dev)
(Intercept)                                                                     
lvm.clusters.zostera.3                 2.773    1.000             2.987    1.000
                       Nototropis.guttatus          Oligochaeta         
                                       Dev Pr(>Dev)         Dev Pr(>Dev)
(Intercept)                                                             
lvm.clusters.zostera.3               7.095    0.879      27.378    0.004
                       Paradoneis.harpagonea          Parthenina.interstincta         
                                         Dev Pr(>Dev)                     Dev Pr(>Dev)
(Intercept)                                                                           
lvm.clusters.zostera.3                 1.386    1.000                   2.884    1.000
                       Parvicardium.exiguum          Perinereis.cultrifera         
                                        Dev Pr(>Dev)                   Dev Pr(>Dev)
(Intercept)                                                                        
lvm.clusters.zostera.3                2.911    1.000                 4.654    0.991
                       Perioculodes.longimanus          Phoronida         
                                           Dev Pr(>Dev)       Dev Pr(>Dev)
(Intercept)                                                               
lvm.clusters.zostera.3                   4.365    0.994     5.372    0.983
                       Phyllodoce.sp.          Platyhelminthes         
                                  Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                            
lvm.clusters.zostera.3          4.159    1.000           5.906    0.957
                       Platynereis.dumerilii          Polititapes.aureus         
                                         Dev Pr(>Dev)                Dev Pr(>Dev)
(Intercept)                                                                      
lvm.clusters.zostera.3                 8.537    0.700              4.065    1.000
                       Polychaeta.larvae          Polydora.ciliata         
                                     Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                
lvm.clusters.zostera.3             4.159    1.000           29.489    0.002
                       Polygordius.neapolitanus          Prionospio.cirrifera         
                                            Dev Pr(>Dev)                  Dev Pr(>Dev)
(Intercept)                                                                           
lvm.clusters.zostera.3                    4.159    1.000               41.351    0.001
                       Protodorvillea.kefersteini          Pseudocuma.longicorne
                                              Dev Pr(>Dev)                   Dev
(Intercept)                                                                     
lvm.clusters.zostera.3                     25.261    0.004                 1.726
                                Rissoa.membranacea          Rissoa.splendida         
                       Pr(>Dev)                Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                          
lvm.clusters.zostera.3    1.000              1.701    1.000           17.118    0.058
                       Salvatoria.clavata          Schistomeringos.rudolphi         
                                      Dev Pr(>Dev)                      Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.3             32.959    0.002                    5.024    0.985
                       Sphaerosyllis.hystrix          Spio.filicornis         
                                         Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                                   
lvm.clusters.zostera.3                12.736    0.216          34.632    0.002
                       Spisula.subtruncata          Stenosoma.capito         
                                       Dev Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                                                  
lvm.clusters.zostera.3               5.885    0.957            7.189    0.879
                       Syllis.gracilis          Syllis.hyalina          Tellina.tenuis
                                   Dev Pr(>Dev)            Dev Pr(>Dev)            Dev
(Intercept)                                                                           
lvm.clusters.zostera.3          10.712    0.407          4.555    0.992          3.112
                                Thracia.phaseolina          Tricolia.pullus         
                       Pr(>Dev)                Dev Pr(>Dev)             Dev Pr(>Dev)
(Intercept)                                                                         
lvm.clusters.zostera.3    1.000              2.773    1.000          13.288    0.176
                       Tritia.neritea          Tritia.reticulata          Turbellaria
                                  Dev Pr(>Dev)               Dev Pr(>Dev)         Dev
(Intercept)                                                                          
lvm.clusters.zostera.3          2.037    1.000             2.932    1.000       1.527
                                Upogebia.pusilla         
                       Pr(>Dev)              Dev Pr(>Dev)
(Intercept)                                              
lvm.clusters.zostera.3    1.000           10.026    0.493
Arguments:
 Test statistics calculated assuming uncorrelated response (for faster computation) 
P-value calculated using 999 resampling iterations via PIT-trap resampling (to account for correlation in testing.

Save the ANOVA, too.

write_rds(glms.lvm.zostera.3.aov, 
          here(save.dir, "glms_lvm_zostera_3_anova.RDS"))

NOW let’s get the taxa with the highest contributions to the tested pattern.

## get the top contributing species for the initial zostera GLMs 
(top.sp.glms.lvm.zostera.3 <- top_n_sp_glm(glms.lvm.zostera.3.aov, tot.dev.expl = 0.75)
)
[1] "Total deviance explained: 0.82"
    Apseudopsis.ostroumovi       Prionospio.cirrifera  Monocorophium.acherusicum 
                 51.413970                  41.350974                  39.678240 
       Mytilaster.lineatus            Spio.filicornis        Bittium.reticulatum 
                 34.909870                  34.632433                  34.188511 
          Cumella.limicola         Salvatoria.clavata         Capitella.capitata 
                 33.633823                  32.958829                  30.336457 
          Polydora.ciliata        Loripes.orbiculatus                  Abra.alba 
                 29.489490                  28.175552                  27.437828 
               Oligochaeta           Chamelea.gallina Protodorvillea.kefersteini 
                 27.378351                  27.138297                  25.260955 
           Melinna.palmata          Ampelisca.diadema    Heteromastus.filiformis 
                 24.202974                  20.153373                  17.463258 
          Rissoa.splendida    Amphibalanus.improvisus        Leiochone.leiopygos 
                 17.117581                  15.231072                  14.994968 
 Microdeutopus.gryllotalpa            Alitta.succinea            Tricolia.pullus 
                 13.746930                  13.527612                  13.287785 
     Sphaerosyllis.hystrix         Microphthalmus.sp.            Syllis.gracilis 
                 12.736427                  11.854688                  10.711746 
              Lagis.koreni           Upogebia.pusilla        Chironomidae.larvae 
                 10.471907                  10.025894                   9.650905 
      Harmothoe.reticulata      Kellia.suborbicularis               Ampithoe.sp. 
                  9.416160                   8.973262                   8.726571 
     Platynereis.dumerilii                Glycera.sp.            Exogone.naidina 
                  8.536643                   7.992056                   7.227403 
          Stenosoma.capito        Nototropis.guttatus           Capitella.minima 
                  7.189015                   7.094867                   6.793482 
Micromaldane.ornithochaeta 
                  6.655076 
## unfortunately, mvabund likes to rename my species when converting the data to matrix (no spaces in names), and since I'm going to look them up in my initial untransformed count data, I have to change them back..   
names(top.sp.glms.lvm.zostera.3) <- names(top.sp.glms.lvm.zostera.3) %>% 
  str_replace(pattern = "\\.", replacement = " ")
top.sp.glms.lvm.zostera.3
    Apseudopsis ostroumovi       Prionospio cirrifera  Monocorophium acherusicum 
                 51.413970                  41.350974                  39.678240 
       Mytilaster lineatus            Spio filicornis        Bittium reticulatum 
                 34.909870                  34.632433                  34.188511 
          Cumella limicola         Salvatoria clavata         Capitella capitata 
                 33.633823                  32.958829                  30.336457 
          Polydora ciliata        Loripes orbiculatus                  Abra alba 
                 29.489490                  28.175552                  27.437828 
               Oligochaeta           Chamelea gallina Protodorvillea kefersteini 
                 27.378351                  27.138297                  25.260955 
           Melinna palmata          Ampelisca diadema    Heteromastus filiformis 
                 24.202974                  20.153373                  17.463258 
          Rissoa splendida    Amphibalanus improvisus        Leiochone leiopygos 
                 17.117581                  15.231072                  14.994968 
 Microdeutopus gryllotalpa            Alitta succinea            Tricolia pullus 
                 13.746930                  13.527612                  13.287785 
     Sphaerosyllis hystrix         Microphthalmus sp.            Syllis gracilis 
                 12.736427                  11.854688                  10.711746 
              Lagis koreni           Upogebia pusilla        Chironomidae larvae 
                 10.471907                  10.025894                   9.650905 
      Harmothoe reticulata      Kellia suborbicularis               Ampithoe sp. 
                  9.416160                   8.973262                   8.726571 
     Platynereis dumerilii                Glycera sp.            Exogone naidina 
                  8.536643                   7.992056                   7.227403 
          Stenosoma capito        Nototropis guttatus           Capitella minima 
                  7.189015                   7.094867                   6.793482 
Micromaldane ornithochaeta 
                  6.655076 

Try to plot these top contributing species - for whatever that’s worth, because 50 species on a plot is still a monstrosity.

## get the species and their abundances from the original count data, and transform them to long format
(abnd.top.sp.glms.lvm.zostera.3 <- zoo.abnd.zostera %>% 
   select(station, names(top.sp.glms.lvm.zostera.3)) %>% 
   gather(key = "species", value = "count", -station) %>% 
   ## turn species into a factor, or you'll be very very sorry later, when they're out of order on the plot. NB need to be in REVERSE order, because ggplot plots from bottom to top, and I want the top-contributing species on top. 
   mutate(species = factor(species, levels = rev(names(top.sp.glms.lvm.zostera.3))))
)
(plot.top.sp.glms.lvm.zostera.3 <- plot_top_n(abnd.top.sp.glms.lvm.zostera.3,
                                              mapping = aes(x = species, y = log_y_min(count), colour = station),
                                              labs.legend = paste0("Z", as.numeric(unique(abnd.top.sp.glms.lvm.zostera.3$station))),
                                              lab.y = "Abundance (log(y/min + 1))",
                                              palette = "Set2"
                                        ) +
    theme(legend.position = "top")
)

Extract the top-contributing species to each cluster (this same nightmare above, but as a table). This chunk is STILL hopelessly ugly and clumsy.

top.sp.abnd.glms.lvm.zostera.3 <- lapply(names(glms.lvm.zostera.3.summary$aliased), function(x) top_sp_glms_table(glms.lvm.zostera.3.summary, x, p = 0.05)) 
## fix species names (remove dot) 
top.sp.abnd.glms.lvm.zostera.3 <- lapply(top.sp.abnd.glms.lvm.zostera.3, function(x) x %>% mutate(species = str_replace(species, pattern = "\\.", replacement = " ")))
## rename columns (= group names) - right now they are something like "lvm.clusters.zostera3" etc.
top.sp.abnd.glms.lvm.zostera.3 <- lapply(top.sp.abnd.glms.lvm.zostera.3, function(x) x %>% rename_at(vars(contains("lvm.clusters.zostera.3")), list(~str_replace_all(., pattern = "lvm.clusters.zostera.3", "group_"))))
top.sp.abnd.glms.lvm.zostera.3 <- lapply(top.sp.abnd.glms.lvm.zostera.3, function(x) x %>% rename_at(vars(contains("Intercept")), list(~str_replace_all(., pattern = "\\(Intercept\\)", "group_1"))))
## pull the abundances from the original count df and add to the summary glm tables 
## make a long df of abundances & add clusters  
zoo.abnd.zostera.long.3 <- zoo.abnd.zostera %>%
  select(-c(month:replicate)) %>%
  gather(key = "species", value = "count", -station) %>% 
  mutate(group = case_when(station %in% c("Poda", "Otmanli") ~ 1,
                           station == "Vromos" ~ 2, 
                           station == "Gradina" ~ 3, 
                           station == "Ropotamo" ~ 4)
         )
## sum sp abundances by group; nest by group
zoo.abnd.zostera.long.3.smry <- zoo.abnd.zostera.long.3 %>% 
  group_by(species, group) %>% 
  summarise(total_count = sum(count)) %>% 
  group_by(group) %>%
  nest()
## add the counts to the group dfs - wow that's an ugly, ugly hack. Wish I had more time to write this up properly.. 
top.sp.abnd.glms.lvm.zostera.3 <- map2(top.sp.abnd.glms.lvm.zostera.3, zoo.abnd.zostera.long.3.smry %>% pull(group), ~left_join(.x, zoo.abnd.zostera.long.3.smry %>% filter(group == .y) %>% unnest(), by = "species"))
## since these are sum counts over all the replicates (that's why the monstrous numbers), average them to be mean counts per group. NB different groups consist of different numbers of replicates, b.c. some groups consist of more than one station
(top.sp.abnd.glms.lvm.zostera.3 <- map2(top.sp.abnd.glms.lvm.zostera.3, c(16, 4, 8, 4), function(x, y) x %>% mutate(mean_count = total_count/y))
)
[[1]]

[[2]]

[[3]]

[[4]]
NA

In the case of the seagrasses and case 3 clusters, the picture is still more confusing..
The LRs seem to be a bit lower for groups 2 and 3, maybe 4 too - still not sure if you can use that as a significance measure.
For now, in group 1 (= Z1-Z2), the species/taxa with significantly higher abundance are: Bittium reticulatum, Capitella minima, Oligochaeta, Heteromastus filiformis, Polydora ciliata, Prionosprio cirrifera, Rissoa membranacea, Abra alba, Ampelisca diadema (+ others, medium abundance); and the ones with a significantly lower abundance - or even absent - S. clavata, A. ostroumovi, C. gallina, T. pullus.
There are more species singled out for this cluster, probably because of the variability between the two years of sampling.
For group 2 (= Z3), the species with higher abundance are: M. acherusicum, S. filicornis, A. diadema. The species with lower abundance - in fact 0 - are B. reticulatum, P. cirrifera, S. clavata, A. alba, P. ciliata, oligochaetes, H. filiformis, R. splendida.
For group 3 (= Z4), the species with higher abundance are: M. lineatus, less so - C. limicola, L. orbiculatus, P. kefersteini, C. capitata, etc. The species with lower abundance (or 0) are: P. cirrifera, P. ciliata, A. alba, etc.
For group 4 (= Z5), the species with higher abundance are: A. ostoumovi, C. capitata, oligochaetes (very abundant, but with a small LR - nice!). The species with lower abundance (or 0) are: R. splendida, S. clavata, C. limicola.

All in all, I think that group 1 (Poda + Otmanli) holds, and so does group 2 (Vromos). The question is whether it makes sense to separate Gradina and Ropotamo into 2 groups, or if they make more sense together. Ropotamo is characterized by a very high number of oligochaetes, while Gradina’s most distinguishing characteristic is the high number of M. lineatus - mostly very small ones, attached to the rhizomes, close to the sediment surface I presume. Both stations have C. limicola in medium abundance, which is not present anywhere else.

Try to compare the three models..

glms.lvm.zostera.comp
Analysis of Deviance Table

glms.lvm.zostera.1: zoo.mvabnd.zostera ~ lvm.clusters.zostera.1
glms.lvm.zostera.3: zoo.mvabnd.zostera ~ lvm.clusters.zostera.3
glms.lvm.zostera.2: zoo.mvabnd.zostera ~ lvm.clusters.zostera.2

Multivariate test:
                   Res.Df Df.diff   Dev Pr(>Dev)    
glms.lvm.zostera.1     29                           
glms.lvm.zostera.3     28       1 262.1    0.002 ** 
glms.lvm.zostera.2     27       1 256.8    0.001 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Univariate Tests:
                   Abra.alba          Abra.sp.          Actiniaria         
                         Dev Pr(>Dev)      Dev Pr(>Dev)        Dev Pr(>Dev)
glms.lvm.zostera.1                                                         
glms.lvm.zostera.3     1.506    0.999        0    1.000          0    1.000
glms.lvm.zostera.2     0.023    1.000        0    1.000      1.386    1.000
                   Alitta.succinea          Ampelisca.diadema         
                               Dev Pr(>Dev)               Dev Pr(>Dev)
glms.lvm.zostera.1                                                    
glms.lvm.zostera.3           4.881    0.681             0.094    1.000
glms.lvm.zostera.2          23.057    0.001            10.416    0.115
                   Amphibalanus.improvisus          Ampithoe.sp.         
                                       Dev Pr(>Dev)          Dev Pr(>Dev)
glms.lvm.zostera.1                                                       
glms.lvm.zostera.3                   0.349    1.000        2.405    0.970
glms.lvm.zostera.2                   8.177    0.274        3.482    0.937
                   Anadara.kagoshimensis          Apherusa.bispinosa         
                                     Dev Pr(>Dev)                Dev Pr(>Dev)
glms.lvm.zostera.1                                                           
glms.lvm.zostera.3                     0    1.000              0.811    1.000
glms.lvm.zostera.2                 1.386    1.000                  0    1.000
                   Apseudopsis.ostroumovi          Bittium.reticulatum         
                                      Dev Pr(>Dev)                 Dev Pr(>Dev)
glms.lvm.zostera.1                                                             
glms.lvm.zostera.3                 20.559    0.003               3.006    0.943
glms.lvm.zostera.2                   1.38    1.000               0.004    1.000
                   Brachynotus.sexdentatus          Capitella.capitata         
                                       Dev Pr(>Dev)                Dev Pr(>Dev)
glms.lvm.zostera.1                                                             
glms.lvm.zostera.3                   0.811    1.000              4.124    0.797
glms.lvm.zostera.2                   1.386    1.000              2.862    0.965
                   Capitella.minima          Chamelea.gallina         
                                Dev Pr(>Dev)              Dev Pr(>Dev)
glms.lvm.zostera.1                                                    
glms.lvm.zostera.3            6.055    0.509            0.908    1.000
glms.lvm.zostera.2            0.433    1.000            1.386    0.996
                   Chironomidae.larvae          Cumella.limicola         
                                   Dev Pr(>Dev)              Dev Pr(>Dev)
glms.lvm.zostera.1                                                       
glms.lvm.zostera.3               5.456    0.616            1.089    1.000
glms.lvm.zostera.2                   0    1.000            7.694    0.334
                   Cumella.pygmaea          Cytharella.costulata         
                               Dev Pr(>Dev)                  Dev Pr(>Dev)
glms.lvm.zostera.1                                                       
glms.lvm.zostera.3           1.891    0.995                0.073    1.000
glms.lvm.zostera.2               0    1.000                4.159    0.859
                   Diogenes.pugilator          Eteone.flava          Eunice.vittata
                                  Dev Pr(>Dev)          Dev Pr(>Dev)            Dev
glms.lvm.zostera.1                                                                 
glms.lvm.zostera.3              1.483    1.000            0    1.000            2.7
glms.lvm.zostera.2               0.68    1.000            0    1.000          0.208
                            Eurydice.dollfusi          Exogone.naidina         
                   Pr(>Dev)               Dev Pr(>Dev)             Dev Pr(>Dev)
glms.lvm.zostera.1                                                             
glms.lvm.zostera.3    0.963             1.891    0.995           1.284    1.000
glms.lvm.zostera.2    1.000                 0    1.000            1.25    1.000
                   Gastrosaccus.sanctus          Genetyllis.tuberculata         
                                    Dev Pr(>Dev)                    Dev Pr(>Dev)
glms.lvm.zostera.1                                                              
glms.lvm.zostera.3                0.811    1.000                  1.499    0.999
glms.lvm.zostera.2                    0    1.000                  5.746    0.594
                   Glycera.sp.          Glycera.tridactyla          Glycera.unicornis
                           Dev Pr(>Dev)                Dev Pr(>Dev)               Dev
glms.lvm.zostera.1                                                                   
glms.lvm.zostera.3           0    1.000                  0    1.000                 0
glms.lvm.zostera.2           0    1.000              1.033    1.000             1.386
                            Harmothoe.imbricata          Harmothoe.reticulata         
                   Pr(>Dev)                 Dev Pr(>Dev)                  Dev Pr(>Dev)
glms.lvm.zostera.1                                                                    
glms.lvm.zostera.3    1.000               1.352    1.000                4.286    0.775
glms.lvm.zostera.2    1.000               5.561    0.600                5.794    0.583
                   Heteromastus.filiformis          Hirudinea          Hydrobia.acuta
                                       Dev Pr(>Dev)       Dev Pr(>Dev)            Dev
glms.lvm.zostera.1                                                                   
glms.lvm.zostera.3                   7.242    0.344     0.811    1.000              0
glms.lvm.zostera.2                  10.679    0.104         0    1.000          1.494
                            Hydrobia.sp.          Iphinoe.tenella         
                   Pr(>Dev)          Dev Pr(>Dev)             Dev Pr(>Dev)
glms.lvm.zostera.1                                                        
glms.lvm.zostera.3    1.000        0.569    1.000            1.31    1.000
glms.lvm.zostera.2    0.996        3.709    0.931           4.354    0.838
                   Kellia.suborbicularis          Lagis.koreni         
                                     Dev Pr(>Dev)          Dev Pr(>Dev)
glms.lvm.zostera.1                                                     
glms.lvm.zostera.3                 4.389    0.773        0.767    1.000
glms.lvm.zostera.2                 0.104    1.000        5.999    0.563
                   Leiochone.leiopygos          Lentidium.mediterraneum         
                                   Dev Pr(>Dev)                     Dev Pr(>Dev)
glms.lvm.zostera.1                                                              
glms.lvm.zostera.3               8.777    0.191                   1.622    0.999
glms.lvm.zostera.2               0.336    1.000                       0    1.000
                   Lepidochitona.cinerea          Loripes.orbiculatus         
                                     Dev Pr(>Dev)                 Dev Pr(>Dev)
glms.lvm.zostera.1                                                            
glms.lvm.zostera.3                 0.811    1.000               2.917    0.946
glms.lvm.zostera.2                     0    1.000               3.172    0.942
                   Lucinella.divaricata          Magelona.papillicornis         
                                    Dev Pr(>Dev)                    Dev Pr(>Dev)
glms.lvm.zostera.1                                                              
glms.lvm.zostera.3                1.915    0.995                  0.811    1.000
glms.lvm.zostera.2                    0    1.000                      0    1.000
                   Maldane.glebifex          Melinna.palmata         
                                Dev Pr(>Dev)             Dev Pr(>Dev)
glms.lvm.zostera.1                                                   
glms.lvm.zostera.3                0    1.000               0    1.000
glms.lvm.zostera.2            1.386    0.998           2.657    0.985
                   Microdeutopus.gryllotalpa          Micromaldane.ornithochaeta
                                         Dev Pr(>Dev)                        Dev
glms.lvm.zostera.1                                                              
glms.lvm.zostera.3                    10.659    0.084                      2.111
glms.lvm.zostera.2                     2.603    0.985                          0
                            Micronephthys.stammeri          Microphthalmus.fragilis
                   Pr(>Dev)                    Dev Pr(>Dev)                     Dev
glms.lvm.zostera.1                                                                 
glms.lvm.zostera.3    0.995                  2.197    0.994                       0
glms.lvm.zostera.2    1.000                  1.386    1.000                   1.494
                            Microphthalmus.sp.          Monocorophium.acherusicum
                   Pr(>Dev)                Dev Pr(>Dev)                       Dev
glms.lvm.zostera.1                                                               
glms.lvm.zostera.3    1.000              2.459    0.970                      1.35
glms.lvm.zostera.2    0.996                  0    1.000                     0.213
                            Mytilaster.lineatus          Mytilus.galloprovincialis
                   Pr(>Dev)                 Dev Pr(>Dev)                       Dev
glms.lvm.zostera.1                                                                
glms.lvm.zostera.3    1.000              12.977    0.028                         0
glms.lvm.zostera.2    1.000              12.953    0.043                     1.386
                            Nemertea          Nephtys.cirrosa         
                   Pr(>Dev)      Dev Pr(>Dev)             Dev Pr(>Dev)
glms.lvm.zostera.1                                                    
glms.lvm.zostera.3    1.000    1.013    1.000           0.811    1.000
glms.lvm.zostera.2    1.000    5.479    0.640           1.386    1.000
                   Nephtys.kersivalensis          Nereis.perivisceralis         
                                     Dev Pr(>Dev)                   Dev Pr(>Dev)
glms.lvm.zostera.1                                                              
glms.lvm.zostera.3                     0    1.000                 0.811    1.000
glms.lvm.zostera.2                 1.386    1.000                     0    1.000
                   Nereis.pulsatoria          Nototropis.guttatus          Oligochaeta
                                 Dev Pr(>Dev)                 Dev Pr(>Dev)         Dev
glms.lvm.zostera.1                                                                    
glms.lvm.zostera.3                 0    1.000               4.485    0.744       5.602
glms.lvm.zostera.2             3.251    0.941               0.116    1.000       9.386
                            Paradoneis.harpagonea          Parthenina.interstincta
                   Pr(>Dev)                   Dev Pr(>Dev)                     Dev
glms.lvm.zostera.1                                                                
glms.lvm.zostera.3    0.616                     0    1.000                   0.919
glms.lvm.zostera.2    0.179                 1.386    1.000                   1.662
                            Parvicardium.exiguum          Perinereis.cultrifera         
                   Pr(>Dev)                  Dev Pr(>Dev)                   Dev Pr(>Dev)
glms.lvm.zostera.1                                                                      
glms.lvm.zostera.3    1.000                0.824    1.000                 0.973    1.000
glms.lvm.zostera.2    0.995                0.063    1.000                 2.035    0.994
                   Perioculodes.longimanus          Phoronida          Phyllodoce.sp.
                                       Dev Pr(>Dev)       Dev Pr(>Dev)            Dev
glms.lvm.zostera.1                                                                   
glms.lvm.zostera.3                   2.111    0.995     1.284    1.000              0
glms.lvm.zostera.2                       0    1.000      0.11    1.000              0
                            Platyhelminthes          Platynereis.dumerilii         
                   Pr(>Dev)             Dev Pr(>Dev)                   Dev Pr(>Dev)
glms.lvm.zostera.1                                                                 
glms.lvm.zostera.3    1.000           1.372    1.000                 1.257    1.000
glms.lvm.zostera.2    1.000           2.602    0.985                 0.374    1.000
                   Polititapes.aureus          Polychaeta.larvae         
                                  Dev Pr(>Dev)               Dev Pr(>Dev)
glms.lvm.zostera.1                                                       
glms.lvm.zostera.3              0.751    1.000                 0    1.000
glms.lvm.zostera.2              6.933    0.406                 0    1.000
                   Polydora.ciliata          Polygordius.neapolitanus         
                                Dev Pr(>Dev)                      Dev Pr(>Dev)
glms.lvm.zostera.1                                                            
glms.lvm.zostera.3             13.8    0.016                        0    1.000
glms.lvm.zostera.2           12.416    0.052                        0    1.000
                   Prionospio.cirrifera          Protodorvillea.kefersteini         
                                    Dev Pr(>Dev)                        Dev Pr(>Dev)
glms.lvm.zostera.1                                                                  
glms.lvm.zostera.3               28.158    0.002                      7.725    0.295
glms.lvm.zostera.2                4.922    0.768                      4.879    0.771
                   Pseudocuma.longicorne          Rissoa.membranacea         
                                     Dev Pr(>Dev)                Dev Pr(>Dev)
glms.lvm.zostera.1                                                           
glms.lvm.zostera.3                 0.236    1.000              1.543    0.999
glms.lvm.zostera.2                 1.386    1.000              1.019    1.000
                   Rissoa.splendida          Salvatoria.clavata         
                                Dev Pr(>Dev)                Dev Pr(>Dev)
glms.lvm.zostera.1                                                      
glms.lvm.zostera.3            5.569    0.616             15.955    0.007
glms.lvm.zostera.2                0    1.000                  0    1.000
                   Schistomeringos.rudolphi          Sphaerosyllis.hystrix         
                                        Dev Pr(>Dev)                   Dev Pr(>Dev)
glms.lvm.zostera.1                                                                 
glms.lvm.zostera.3                    2.389    0.972                 0.023    1.000
glms.lvm.zostera.2                    8.799    0.222                 4.024    0.898
                   Spio.filicornis          Spisula.subtruncata         
                               Dev Pr(>Dev)                 Dev Pr(>Dev)
glms.lvm.zostera.1                                                      
glms.lvm.zostera.3           6.523    0.442                   0    1.000
glms.lvm.zostera.2           0.246    1.000                   0    1.000
                   Stenosoma.capito          Syllis.gracilis          Syllis.hyalina
                                Dev Pr(>Dev)             Dev Pr(>Dev)            Dev
glms.lvm.zostera.1                                                                  
glms.lvm.zostera.3            2.178    0.995           4.755    0.709          2.507
glms.lvm.zostera.2            6.661    0.490          17.831    0.004              0
                            Tellina.tenuis          Thracia.phaseolina         
                   Pr(>Dev)            Dev Pr(>Dev)                Dev Pr(>Dev)
glms.lvm.zostera.1                                                             
glms.lvm.zostera.3    0.970          1.622    0.999              0.811    1.000
glms.lvm.zostera.2    1.000          1.386    1.000                  0    1.000
                   Tricolia.pullus          Tritia.neritea          Tritia.reticulata
                               Dev Pr(>Dev)            Dev Pr(>Dev)               Dev
glms.lvm.zostera.1                                                                   
glms.lvm.zostera.3           5.332    0.635          0.632    1.000                 0
glms.lvm.zostera.2            1.38    1.000          3.479    0.937             8.301
                            Turbellaria          Upogebia.pusilla         
                   Pr(>Dev)         Dev Pr(>Dev)              Dev Pr(>Dev)
glms.lvm.zostera.1                                                        
glms.lvm.zostera.3    1.000       1.392    1.000            5.769    0.557
glms.lvm.zostera.2    0.264       1.125    1.000                0    1.000
Arguments:
 Test statistics calculated assuming uncorrelated response (for faster computation) 
P-value calculated using 999 resampling iterations via PIT-trap resampling (to account for correlation in testing.

Well I don’t know how to interpret that.. Have to check the manual first.

---
title: "Multivariate analyses of community structure (modeling)"
date: "2019-03-26"
output: html_notebook
---

This notebook contains all multivariate analyses of zoobenthic community structure using the new, nearly unheard-of modeling methods: packages mvabund, boral.  
Again, to make it self-contained, there will be the same repetitive setup/data import/preparation part.  

***  

Setup!
```{r setup, include = FALSE}
library(knitr)

knit_hooks$set(small.mar = function(before, options, envir) {
    if (before) par(mar = c(2, 2, .1, 2))  # smaller margin on top
})

## set the working directory to one up (all notebooks - kept in their own subdirectory within the project directory).
opts_knit$set(root.dir = rprojroot::find_rstudio_root_file())

## set knitr options for knitting code into the report.
opts_chunk$set(cache = TRUE, # save results so that code blocks aren't re-run unless code changes
               autodep = TRUE, # ..or unless a relevant earlier code block changed
               cache.comments = FALSE, # don't re-run if the only thing that changed was the comments
               highlight = TRUE, 
               small.mar = TRUE)
```

Define the working subdirectories.  
```{r workspace_setup}
## print the working directory, just to be on the safe side
paste("You are here: ", getwd())

data.dir <- "data"    ## input data files
functions.dir <- "R"  ## functions & scripts
save.dir <- "output"  ## clean data, output from models & more complex calculations
figures.dir <- "figs" ## plots & figures 
```

Import libraries.  
```{r import_packages, results = FALSE}
library(here) ## painless relative paths to subdurectories, etc.
library(tidyverse) ## data manipulation, cleaning, aggregation
library(viridis) ## smart & pretty colour schemes
library(mvabund) ## multivariate modeling analyses in ecology
library(boral) ## more multivariate modeling analyses in ecology
```

Organize some commonly-used ggplot2 modifications into a more convenient (and less repetitive) format. One day, I MUST figure out the proper way to set the theme..    
```{r custom_ggplot_settings_helpers}
## ggplot settings & things that I keep reusing
# ggplot_theme <- list(
#   theme_bw(),
#   theme(element_text(family = "Times"))
# )

## always use black-and-white theme
theme_set(theme_bw())

## helper to adjust ggplot text size & avoid repetitions 
text_size <- function(text.x = NULL,
                      text.y = NULL,
                      title.x = NULL,
                      title.y = NULL,
                      legend.text = NULL,
                      legend.title = NULL, 
                      strip.x = NULL, 
                      strip.y = NULL) {
  theme(axis.text.x = element_text(size = text.x),
        axis.text.y = element_text(size = text.y),
        axis.title.x = element_text(size = title.x),
        axis.title.y = element_text(size = title.y),
        legend.text = element_text(size = legend.text), 
        legend.title = element_text(size = legend.title), 
        strip.text.x = element_text(size = strip.x), 
        strip.text.y = element_text(size = strip.y)
        )
}


## log y/min + 1 transform - useful for species counts/biomass data visualization
log_y_min <- function(y) {
  log(y / min(y[y > 0]) + 1)
}

```

***  

#### **Sand stations (Burgas Bay, 2013-2014)**  
Import zoobenthic abundance data (cleaned and prepared).  
```{r import_zoo_abnd_sand}
zoo.abnd.sand <- read_csv(here(save.dir, "abnd_sand_orig_clean.csv"))

## convert station to factor (better safe than sorry later, when the stations are not plotted in the order I want them)
(zoo.abnd.sand <- zoo.abnd.sand %>% 
    mutate(station = factor(station, levels = c("Kraimorie", "Chukalya", "Akin", "Sozopol", "Agalina", "Paraskeva")))
)
```

Remove the all-0 species (= not present in the current dataset).  
Maybe also remove the singletons (species appearing only once in the whole dataset and represented by a single individual = so rare that it's unlikely they carry important information, but it would probably improve the run times).  
```{r filter_zoo_data_sand}
(zoo.abnd.flt.sand <- zoo.abnd.sand %>%
   select(-c(station:replicate)) %>%
   select(which(colSums(.) > 0))
)
```


##### **LVM - model-based ordination**
Perform a model-based unconstrained ordination by fiting a pure latent variable model (package boral - Hui et al., 2014). This will allow to visualize the multivariate stations x species data - similar to nMDS, can be interpreted in the same way.   
I'm including a (fixed) row effect to account for differences in site total abundance - this way, the ordination is in terms of **species composition**.   
NB this takes about a million years to run! 
```{r lvm_sand}
lvm.sand <- boral(y = zoo.abnd.flt.sand, 
                  family = "negative.binomial",
                  
                  ## we want to control for site effects - there are 6 sites with 9 replicates each
                  row.eff = "fixed", row.ids = matrix(rep(1:6, each = 9), ncol = 1),  
                  ## 2 latent variables = 2 axes on which to represent the zoobenthic data
                  lv.control = list(num.lv = 2) 
                  
     #              ## example control structure, to check if function does what I want, because otherwise it takes an intolerably long time, and I'll shoot myself if I have to wait for it again
     #              mcmc.control = list(n.burnin = 10, n.iteration = 100,
     # n.thin = 1)
     #              
     
                  )

```

Check the summary and diagnostic plots for the LVM.  
```{r summary_lvm_sand}
summary(lvm.sand)

## model fit diagnostic plots
plot(lvm.sand) 
```
The residuals plots look fine (no patterns in the residuals vs fitted, so variance is homogeneous, the quantile plot shows a normal distribution of the residuals) - the model fits the data pretty well.  

Save the sand LVM.  
```{r save_lvm_sand}
write_rds(lvm.sand, 
          here(save.dir, "lvm_sand.RDS"))
```

Examine the biplot obtained by fitting the LVM, as well as the 20 most "important" species.   
```{r check_biplot_lvm_sand}
lvsplot(lvm.sand, jitter = T, biplot = TRUE, ind.spp = 20)
```

All in all, the final result resembles the nMDS ordination very much - same 4 clusters (Kraimorie + Chukalya, AKin, Agalina, Sozopol + Paraskeva). Kraimorie and Chukalya are better distinguished on the LVM plot than on the MDS, but still.  
The run time is extremely, extremely long (~1h), but the data don't need to be transformed, and the model fit can be examined and adjusted if necessary.    
The species singled out as significant are probably somewhat different - have to check!   

Redo the biplot, because this one is not very pretty. I'm not adding the species on top, first because I'm too lazy to figure out the procedure for ordering them, and second because the plot gets too busy.   
```{r extract_lvm_coord_sand}
## extract the LV coordinates of the stations from the model, so that the plot can be redone in ggplot 
lvs.coord.sand <- as_tibble(lvm.sand$lv.median)

## add the stations from the original zoobenthic table (order was not modified)
(lvs.coord.sand <- lvs.coord.sand %>% 
  bind_cols(zoo.abnd.sand %>% select(station))
)

```

Make the plot and save it.  
```{r plot_lvm_sand}
(plot.lvm.sand <- ggplot(lvs.coord.sand) + 
    geom_point(aes(x = lv1, y = lv2, colour = station)) + 
    scale_color_brewer(palette = "Set2", name = "station", 
                       labels = paste0("S", as.numeric((unique(lvs.coord.sand %>% pull(station)))))) +
   labs(x = "LV1", y = "LV2")
)

```

```{r save_lvm_plot_sand}
## save the LVM plot for the sand stations
ggsave(file = here(figures.dir, "lvm_sand.png"), 
       plot.lvm.sand, 
       width = 15, units = "cm", dpi = 300)
```


##### **GLM fitting for abundance - environmental data**  
Let's fit GLMs to the sites x species matrix to try and explain the observed differences in community structure by the variation of the environmental parameters.  
These functions all come from package **mvabund**.  
Import the environmental data - the one cleaned, prepared and saved in the previous notebook (classical multivariate methods). It contains long-term averages for the water column data (2009-2011 + 2013-2014) at each station, repeated for each replicate, and the sediment data (2013-2014), again repeated to the same number of replicates. Only the variables determined to be significant by PCA are kept.       
```{r import_env_data_sand} 
env.sand <- read_csv(here(save.dir, "env_data_ordinations_sand.csv"))

## convert station to factor
(env.sand <- env.sand %>% 
    mutate(station = factor(station,
                            levels = c("Kraimorie", "Chukalya", "Akin", "Sozopol", "Agalina", "Paraskeva")))
)
```
Station is a factor, the rest of the variables are numeric.  

Turn the zoobenthic data (minus the all-0 taxa) into a matrix - easier for the mvabund package and methods to deal with.  
```{r matrix_abnd_sand}
## there is already one subset of filtered count data (54 x 147) - use it 
zoo.mvabnd.sand <- mvabund(zoo.abnd.flt.sand)
```

###### **manyGLM by LVM clusters**
First, let's see if the groups from the latent variable model (more or less equal to the clusters from the classical ordination) are valid, and which species exhibit a response.  
```{r clusters_lvm_sand}
## construct the vector of the clusters by hand, it's easier that way.. 
lvm.clusters.sand <- c(rep(1, times = 18), rep(2:4, each = 9), rep(3, times = 9))

## convert to factor
(lvm.clusters.sand <- factor(lvm.clusters.sand))
```

Check the model assumptions. 
1. Mean-variance assumption => determines the choice of family parameter. Can be checked by plotting residuals vs fits: if little pattern - the chosen mean-variance assumption is plausible.  
Another way: direct plotting (variance ~ mean), for each species within each factor
level.  
```{r check_mean_variance_lvm_sand}
plot(manyglm(zoo.mvabnd.sand ~ lvm.clusters.sand, family = "negative.binomial"))

meanvar.plot(zoo.mvabnd.sand ~ lvm.clusters.sand, table = TRUE)
```

It's not perfect, but it's not too terrible either. 

2. Assumed relationship between mean abundance and environmental variables - link function and formula.
When quantitative variables are included in the model (for now, not relevant - will be in the next model) -> if there is a trend in size of residuals at different fitted values (e.g. U-shape,..) = violation of the log-linearity assumption.
  
Everything looks more or less fine; fit the model. 
```{r fit_glms_lvm_sand}
glms.lvm.sand <- manyglm(zoo.mvabnd.sand ~ lvm.clusters.sand, 
                         family = "negative.binomial")

```

Explore the fit (residuals, diagnostic plots, etc.).  
```{r explore_glms_lvm_sand}
## residuals vs fitted values
plot(glms.lvm.sand)


## all traditional (g)lm diagnostic plots
plot.manyglm(glms.lvm.sand, which = 1:3)


### source mvabund GLM plotting functions modified to use a grey palette - I just can't redo these plots on my own, the function is doing too complicated things internally to scale the x and y axes
source(here(functions.dir, "default.plot.manyglm_grey.R"))
source(here(functions.dir, "plot.manyglm_grey.R"))

par(mfrow = c(2,2))
lapply(1:3, function(i) plot.manyglm.grey(glms.lvm.sand, which = i, sub.caption = ""))
par(mfrow = c(1, 1))

```

I really don't like the rainbow palette, but I would like to include these plots in my thesis results.. Will have to do something about it, just not right now.  
Save the model!  
```{r save_glms_lvm_sand}
write_rds(glms.lvm.sand, 
          here(save.dir, "glms_lvm_sand.RDS"))
```

Let's see the model summary (NB takes a LOT of time if there are many resamplings!).  
```{r summary_glms_lvm_sand}
(glms.lvm.sand.summary <- summary(glms.lvm.sand, 
                                  test = "LR", p.uni = "adjusted",
                                  nBoot = 999, ## limit the number of permutations if you just want to check it out
                                  show.time = "all")
)
```

The factor (here - groups outlined by the LVM) is highly significant according to the models.  
This also allows us to see which species exhibit a response to the chosen factor. 
The LR (likelihood ratio) statistic is used as a measure of the strength of individual taxon contributions to the observed patterns. 
I'll save the summary for safekeeping, but I'll also run an anova - to get an analysis of deviance table on the model fit (also better for extracting the species contributions, or at least I know how to do it).  
```{r save_summary_glms_lvm_sand}
write_rds(glms.lvm.sand.summary, 
          here(save.dir, "glms_lvm_sand_summary.RDS"))
```

Run the anova on the model. 
```{r anova_glms_lvm_sand}
(glms.lvm.sand.aov <- anova.manyglm(glms.lvm.sand, 
                                    test = "LR", p.uni = "adjusted", 
                                    nBoot = 999, ## limit the number of permutations for a shorter run time   
                                    show.time = "all") 
)
```
I probably shouldn't have printed all this out, but oh well who cares.  

Save the ANOVA, too.  
```{r save_anova_glms_lvm_sand}
write_rds(glms.lvm.sand.aov, 
          here(save.dir, "glms_lvm_sand_anova.RDS"))
```

NOW let's get the taxa with the highest contributions to the tested pattern (here - clusters in the LVM, which are really the different soft-bottom habitats).  
```{r relative_taxon_contrib_glms_lvm_sand}
top_n_sp_glm <- function(glms.aov, tot.dev.expl = 0.75) {
  ## helper retrieving the top n species with the highest contribution to the patterns tested by the GLMs, in decreasing order.
  ## Arguments: glms.aov - results from an ANOVA on the fitted GLMs
  ##            dev.explained - proportion of explained deviance to use as cutoff
  
  ## get the change in deviance due to the tested pattern (= 2nd row from table of univariate test stats), and sort the species in order of decreasing contribution
  uni.sorted <- sort(glms.aov$uni.test[2, ], decreasing = TRUE, index.return = FALSE)

  ## start at 10 species and check how much of the deviance is explained by their contributions. Repeat, increasing by increments of 10 until the desired explained deviance (set at function call) is reached. 
  top.n.sp <- 10
  dev.expl <- sum(uni.sorted[1:top.n.sp])/sum(uni.sorted)
  
  while(dev.expl < tot.dev.expl) {
    top.n.sp <- top.n.sp + 10
    dev.expl <- sum(uni.sorted[1:top.n.sp])/sum(uni.sorted)
  }
  
  ## print the total deviance explained - just for information
  print(paste("Total deviance explained:", round(dev.expl, 3)))
  
  ## return the final top species (and their univariate contributions, just in case) 
  top.sp <- uni.sorted[1:top.n.sp]
  return(top.sp)
}

## get the top contributing species for the initial sand GLMs 
(top.sp.glms.lvm.sand <- top_n_sp_glm(glms.lvm.sand.aov, tot.dev.expl = 0.75)
)

## unfortunately, mvabund likes to rename my species when converting the data to matrix (no spaces in names), and since I'm going to look them up in my initial untransformed count data, I have to change them back..   
names(top.sp.glms.lvm.sand) <- names(top.sp.glms.lvm.sand) %>% 
  str_replace(pattern = "\\.", replacement = " ")

top.sp.glms.lvm.sand
```

Try to plot these top contributing species - for whatever that's worth, because 50 species on a plot is a monstrosity.  

```{r plot_relative_taxon_contrib_glms_lvm_sand}
## get the species and their abundances from the original count data, and transform them to long format
(abnd.top.sp.glms.lvm.sand <- zoo.abnd.sand %>% 
   select(station, names(top.sp.glms.lvm.sand)) %>% 
   gather(key = "species", value = "count", -station) %>% 
   ## turn species into a factor, or you'll be very very sorry later, when they're out of order on the plot. NB need to be in REVERSE order, because ggplot plots from bottom to top, and I want the top-contributing species on top. 
   mutate(species = factor(species, levels = rev(names(top.sp.glms.lvm.sand))))
)

plot_top_n <- function(top.n.sp.data, mapping, labs.legend, lab.y, palette) {
  ## helper for plotting top n species. Was hoping to avoid repeating it from way back when, but no dice. 
  ## Arguments: top.n.sp.data - data frame (long) of top species' counts/biomasses at the different stations
  ##            mapping - mappings of the aesthetics
  ##            labs.legend - labels the use for the legend entries
  ##            lab.y - custom label for y axis
  ##            palette - custom colour palette (for consistency with other plots)
  
  ggplot(top.n.sp.data, mapping) +
    geom_point(alpha = 0.75) + # make points larger & partially transparent
    scale_color_brewer(palette = palette,  labels = labs.legend) + 
    ylab(lab.y) + 
    coord_flip() 
}


(plot.top.sp.glms.lvm.sand <- plot_top_n(abnd.top.sp.glms.lvm.sand,
                                         mapping = aes(x = species, y = log_y_min(count), colour = station),
                                         labs.legend = paste0("S", as.numeric(unique(abnd.top.sp.glms.lvm.sand$station))),
                                         lab.y = "Abundance (log(y/min + 1))",
                                         palette = "Set2"
                                        ) +
    theme(legend.position = "top")

)
```

Well this is a nightmarish plot.. I'll probably just put this awfulness in a table and call it a day, or play with lvsplot and the modeled ordination plot, if a plot is what's needed.  

Extract the top-contributing species to each cluster (this same nightmare above, but as a table). This chunk is hopelessly ugly and clumsy (and I'll have to repeat it for the seagrass, too!), but I'm tired of being stuck on this. I still have many, MANY more things to do, and more time-consuming ones too..  
```{r table_relative_taxon_contrib_glms_lvm_sand}
top_sp_glms_table <- function(manyglms.obj.smry, group, p = 0.05) {
  ### extracts the top species in a group for which there is an observed effect in a manyglm test, at the specified probability level.
  ### Returns: tibble with the top species for the specified group/cluster, sorted (descending) by univariate LR value of the species, significant at the given p level. 
  
  ## extract the univariate LR coefficients of the species and their p-values 
  sp_univar <- as_tibble(manyglms.obj.smry$uni.test, rownames = "species")
  sp_p <- as_tibble(manyglms.obj.smry$uni.p, rownames = "species")

  ## combine in the same tibble
  sp_all <- left_join(sp_univar, sp_p, by = "species")  
  
  ## rename the columns
  sp_all <- sp_all %>% 
    rename_at(vars(contains(".x")), list(~str_replace_all(., pattern = ".x", ".LR"))) %>% 
    rename_at(vars(contains(".y")), list(~str_replace_all(., pattern = ".y", ".p")))
  
  ## filter only the group/cluster we want, at the p-level we want
  sp_all_flt <- sp_all %>% 
    select(species, contains(group)) %>% 
    filter_at(vars(contains(".p")), all_vars(. < p)) %>%
    arrange_at(vars(contains(".LR")), list(~desc(.)))

}

top.sp.abnd.glms.lvm.sand <- lapply(names(glms.lvm.sand.summary$aliased), function(x) top_sp_glms_table(glms.lvm.sand.summary, x, p = 0.05)) 

## fix species names (remove dot) 
top.sp.abnd.glms.lvm.sand <- lapply(top.sp.abnd.glms.lvm.sand, function(x) x %>% mutate(species = str_replace(species, pattern = "\\.", replacement = " ")))

## rename columns (= group names) - right now they are something like "lvm.clusters.sand2" etc.
top.sp.abnd.glms.lvm.sand <- lapply(top.sp.abnd.glms.lvm.sand, function(x) x %>% rename_at(vars(contains("lvm.clusters.sand")), list(~str_replace_all(., pattern = "lvm.clusters.sand", "group_"))))

top.sp.abnd.glms.lvm.sand <- lapply(top.sp.abnd.glms.lvm.sand, function(x) x %>% rename_at(vars(contains("Intercept")), list(~str_replace_all(., pattern = "\\(Intercept\\)", "group_1"))))


## pull the abundances from the original count df and add to the summary glm tables 
## make a long df of abundances & add clusters  
zoo.abnd.sand.long <- zoo.abnd.sand %>%
  select(-c(month:replicate)) %>%
  gather(key = "species", value = "count", -station) %>% 
  mutate(group = case_when(station %in% c("Kraimorie", "Chukalya") ~ 1, 
                           station == "Akin" ~ 2, 
                           station %in% c("Sozopol", "Paraskeva") ~ 3, 
                           station == "Agalina" ~ 4))

## sum sp abundances by group; nest by group
zoo.abnd.sand.long.smry <- zoo.abnd.sand.long %>% 
  group_by(species, group) %>% 
  summarise(total_count = sum(count)) %>% 
  group_by(group) %>%
  nest()

## add the counts to the group dfs - wow that's an ugly, ugly hack. Wish I had more time to write this up properly.. 
top.sp.abnd.glms.lvm.sand <- map2(top.sp.abnd.glms.lvm.sand, zoo.abnd.sand.long.smry %>% pull(group), ~left_join(.x, zoo.abnd.sand.long.smry %>% filter(group == .y) %>% unnest(), by = "species"))

## since these are sum counts over all the replicates (that's why the monstrous numbers), average them to be mean counts per group. NB different groups consist of different numbers of replicates, b.c. some groups consist of more than one station
(top.sp.abnd.glms.lvm.sand <- map2(top.sp.abnd.glms.lvm.sand, c(18, 9, 18, 9), function(x, y) x %>% mutate(mean_count = total_count/y))
)
```

To determine the relative taxon contribution to patterns: LR statistic - a measure of strength of individual taxon contributions. LR expresses how many times more likely the data are under one model than the other. This likelihood ratio, or equivalently its logarithm, can then be used to compute a p-value, or, compared to a critical value, to decide whether to reject the null model in favour of the alternative model.  

In this case, the model shows which species exhibit a reaction based on the chosen groups - in other words, which species are more likely to be more/less abundant in each group.  
For **group 1** (= S1-S2), the species/taxa with significantly **higher abundance** are: Oligochaeta, H. filiformis, P. kefersteini, M. palmata, P. cirrifera, A. diadema (among others); and the ones with significantly **lower abundance** - even 0, in some cases - S. bidentata, B.lanceolatum, M. papillicornis, Melita palmata, P. jubatus, and so on.  
For **group 2** (= S3), the species with **higher abundance** are: B. lanceolatum, O. limacina, Oligochaeta (this is this strange artifact of 2013), P. kefersteini, L. flavocapitatus. The species with **lower abundance** are: H. filiformis, A. kagoshimensis, M. stammeri, Melinna palmata, etc.
For **group 3** (= S4-S6), the species with **higher abundance** are: C. gallina, L. mediterraneum - with very high dominance over practically all others; also Pseudocuma longicorne, Spio filicornis. The species with **lower abundance** are: H. filiformis, Oligochaetes (to a certain extent - they are still present, though), A. kagoshimensis, L. koreni, Harmothoe reticulata, Iphinoe tenella, Leiochone leiopygos.  
For **group 4** (= S5), the species with **higher abundance** are: Microdeutopus versiculatus, Eurydice dollfusi, Melita palmata, Polygordius neapolitanus, Polycirrus caliendrum, Polycirrus jubatus, Streptosyllis bidentata. The species with **lower abundance** are: A. kagoshimensis, Melinna palmata, P. cirrifera, P. ciliata, A. alba, I. tenella.   
I love how the species with the highest variances (e.g. C. gallina, the most conspicuous example) are consistently pushed back - have lower LR scores. This is very good - C. gallina in particular is dominant in group 3, but is present also in all other groups - its substrate/depth preferences are very wide, so this is not uncommon. It's not automatically pushed to the top of the list, but its reaction is detected by the manyGLM test. Neat! 
Contrast to the SIMPER results, where the species with the highest variance are consistently at the top - they contribute the most to the similarity, as per the test definition.  

I'm going to save these as separate files (manually), then format them as tables - I know it's a shame, but I'm too frustrated to figure out how to do it programmatically.  
I'll also put them in a word table in my final text, because I don't want to deal with a million separate ones (embedded excel tables don't split over multiple pages).  

**NB In my text, I'm switching the names/places of group 3 and 4, to be consistent with the SIMPER groups (I'm NOT going to repeat all this just to have the numbers match up). So the file names, table names, etc. remain as above. But in the text, I'll have the following: group 1 = S1-S2, group 2 = S3, group 3 = S5, group 4 = S4-S6. REMEMBER THIS SO THERE IS NO CONFUSION!**


###### **manyGLM by environmental parameters**  
Now, let's try to see a different thing - which environmental parameters best describe the species response.  
I'm going to use the PCA-filtered environmental data - it's still going to be a slog, with 7 potential predictors..  
First, construct the formula for the model - will do it separately in case I need to update it later, etc.  
```{r formula_env_manyglm_sand}
(formula.env.glms.sand <- formula(paste("zoo.mvabnd.sand ~", 
                                        paste(env.sand %>% select(-station) %>% names(), collapse = "+")))
)
```

Fit the GLMs to the sand abundance data. 
```{r fit_glms_env_sand}
env.glms.sand <- manyglm(formula.env.glms.sand,
                         data = env.sand,
                         family = "negative.binomial")

```

Explore the fit (residuals, diagnostic plots, etc.).  
```{r explore_glms_env_sand}
## residuals vs fitted values
plot(env.glms.sand)


## all traditional (g)lm diagnostic plots
plot.manyglm(env.glms.sand, which = 1:3)


# ### source mvabund GLM plotting functions modified to use a grey palette - I just can't redo these plots on my own, the function is doing too complicated things internally to scale the x and y axes
# source(here(functions.dir, "default.plot.manyglm_grey.R"))
# source(here(functions.dir, "plot.manyglm_grey.R"))
# 
# par(mfrow = c(2,2))
# lapply(1:3, function(i) plot.manyglm.grey(glms.lvm.sand, which = i, sub.caption = ""))
# par(mfrow = c(1, 1))

```

Well, it's good enough if you ask me (still the kinda strange "line" at lin.pred = -6; otherwise residuals are random enough).  

Save the model!  
```{r save_glms_env_sand}
write_rds(env.glms.sand, 
          here(save.dir, "glms_env_sand.RDS"))
```

Run the anova on the model - I want to see which predictors best explain the species abundance patterns I have. This is one function that would greatly benefit from being run in parallel.. 
```{r anova_glms_env_sand}
(env.glms.sand.aov <- anova.manyglm(env.glms.sand, 
                                    test = "LR", p.uni = "adjusted", 
                                    nBoot = 999, ## limit the number of permutations for a shorter run time   
                                    show.time = "all") 
)
```

The results suggest that the **long-term average water column parameters** have a major influence on the observed community structure; also the **sediment TOM**, and (marginally) the **sediment composition** (gravel content).  
Save the ANOVA - I really, really don't want to have to repeat it.  
```{r save_anova_glms_env_sand}
write_rds(env.glms.sand.aov, 
          here(save.dir, "glms_env_sand_anova.RDS"))
```

Get the taxa with the highest contributions to the tested pattern (here - species most affected by changes in water/environmental quality parameters).  
```{r relative_taxon_contrib_glms_env_sand}
## get the top contributing species for the environmental parameter sand GLMs 
(top.sp.glms.env.sand <- top_n_sp_glm(env.glms.sand.aov, tot.dev.expl = 0.75)
)

## unfortunately, mvabund likes to rename my species when converting the data to matrix (no spaces in names), and since I'm going to look them up in my initial untransformed count data, I have to change them back..   DON'T BE IN A HURRY TO DO THAT IF YOU WANT TO SUBSET THE ORIGINAL MATRIX BEFORE RUNNING TRAITGLM 
names(top.sp.glms.env.sand) <- names(top.sp.glms.env.sand) %>% 
  str_replace(pattern = "\\.", replacement = " ")

```

I'm going to plot these top contributing species, but I'm not using the plot. At least this time it's more manageable, but still not presentable enough.. 

```{r plot_relative_taxon_contrib_glms_env_sand}
## get the species and their abundances from the original count data, and transform them to long format
(abnd.top.sp.glms.env.sand <- zoo.abnd.sand %>% 
   select(station, names(top.sp.glms.env.sand)) %>% 
   gather(key = "species", value = "count", -station) %>% 
   ## turn species into a factor, or you'll be very very sorry later, when they're out of order on the plot. NB need to be in REVERSE order, because ggplot plots from bottom to top, and I want the top-contributing species on top. 
   mutate(species = factor(species, levels = rev(names(top.sp.glms.env.sand)))) %>% 
   ## add clusters from LVM as a column
   mutate(group = case_when(station %in% c("Kraimorie", "Chukalya") ~ 1, 
                            station == "Akin" ~ 2, 
                            station %in% c("Sozopol", "Paraskeva") ~ 3, 
                            station == "Agalina" ~ 4))
)


(plot.top.sp.glms.env.sand <- plot_top_n(abnd.top.sp.glms.env.sand,
                                         mapping = aes(x = species, y = log_y_min(count), colour = factor(group)),
                                         group = abnd.top.sp.glms.env.sand %>% pull(group), 
                                         labs.legend = unique(abnd.top.sp.glms.env.sand$group),
                                         lab.y = "Abundance (log(y/min + 1))",
                                         palette = "Set2"
                                        ) + 
    theme(legend.position = "top")

)
```


Maybe a bit later I'll try to get this nightmare above as a table... 


Final analysis to try: which species respond differently to different environmental parameters?
(= traits analysis - fit single predictive model for all species at all sites, but w/o attempting to explain the different responses using traits - the species ID is used in place of a traits matrix).  
NB only use the top species that exhibited a reaction in the environmental model fit (= the ones accounting for ~75% of the total variability), and only the significant predictors - to improve run times.   
```{r sp_response_glms_env_sand}
sp.response.glms.env.sand <- traitglm(L = zoo.mvabnd.sand[, names(top.sp.glms.env.sand)], 
                                      R = as.matrix(env.sand %>% select(NH4, NO3, PO4, seston, secchi, TOM, gravel)), 
                                      method = "manyglm")


sp.response.glms.env.sand$fourth.corner


# plot this 
a <- max(abs(sp.response.glms.env.sand$fourth.corner))
colort <- colorRampPalette(c("blue","white","red")) 
plot.spp <- lattice::levelplot(t(as.matrix(sp.response.glms.env.sand$fourth.corner)), xlab = "Environmental Variables",
                     ylab = "Species", col.regions = colort(100), at = seq(-a, a, length = 100),
                     scales = list(x = list(rot = 45)))
print(plot.spp)


```

When using LASSO (method = "glm1path"), the algorithm fails to converge - I'm not sure how to interpret it.. Maybe because the function tests each individual species:env.parameter interaction (does it really??), and none of them by themselves are sufficient to explain a species' response. Not to mention the fact that the samples are not really independent (they are replicates at 6 sites, repeated 3 times).  
When using method = "manyglm", the result is the one shown above. It's still a bitch to interpret - for example, what is the interpretation of an increase in abundance with both high PO4 and Secchi? Or with high NH4, but low NO3? Where are these conditions ever met?   

In fact, everything points towards the conclusion that a species response is determined by a combination of eutrophication parameters in its environment (water column characteristics), and the composition of the sediments (organic matter and granulometry).  
This is actually exactly the same thing that the PERMANOVA gives, in this particular case. However, in the future, I'm leaning more towards the modeling approach - it allows you to check the model fit to one's real data; also, there are no data reductions due to calculation of distance matrices.  




#### **Seagrass stations (Burgas Bay, 2013-2014)**  
Import zoobenthic abundance data (cleaned and prepared).  
```{r import_zoo_abnd_zostera}
zoo.abnd.zostera <- read_csv(here(save.dir, "abnd_zostera_orig_clean.csv"))

## convert station to factor (better safe than sorry later, when the stations are not plotted in the order I want them)
(zoo.abnd.zostera <- zoo.abnd.zostera %>% 
    mutate(station = factor(station, levels = c("Poda", "Otmanli", "Vromos", "Gradina", "Ropotamo")))
)
```

Remove the all-0 species (= not present in the current dataset).  
Maybe also remove the singletons (species appearing only once in the whole dataset and represented by a single individual = so rare that it's unlikely they carry important information, but it would probably improve the run times).  
```{r filter_zoo_data_zostera}
(zoo.abnd.flt.zostera <- zoo.abnd.zostera %>%
   select(-c(station:replicate)) %>%
   select(which(colSums(.) > 0))
)
```


##### **LVM - model-based ordination**
Perform a model-based unconstrained ordination by fiting a pure latent variable model (package boral - Hui et al., 2014). This will allow to visualize the multivariate stations x species data - similar to nMDS, can be interpreted in the same way.   
I'm including a (fixed) row effect to account for differences in site total abundance - this way, the ordination is in terms of **species composition**.   
NB this takes about a million years to run! 
```{r lvm_zostera}
lvm.zostera <- boral(y = zoo.abnd.flt.zostera, 
                  family = "negative.binomial",
                  
                  ## we want to control for site effects - there are 6 sites with 9 replicates each
                  row.eff = "fixed", row.ids = matrix(rep(1:5, times = c(8, 8, 4, 8, 4)), ncol = 1),  
                  ## 2 latent variables = 2 axes on which to represent the zoobenthic data
                  lv.control = list(num.lv = 2) 
                  
     #              ## example control structure, to check if function does what I want, because otherwise it takes an intolerably long time, and I'll shoot myself if I have to wait for it again
     #              mcmc.control = list(n.burnin = 10, n.iteration = 100,
     # n.thin = 1)
     #              
     
                  )

```

Check the summary and diagnostic plots for the LVM.  
```{r summary_lvm_zostera}
summary(lvm.zostera)

## model fit diagnostic plots
plot(lvm.zostera) 
```
The residuals plots look fine (no patterns in the residuals vs fitted, so variance is homogeneous, the quantile plot shows a (more or less) normal distribution of the residuals) - the model fits the data pretty well.  

Save the zostera LVM.  
```{r save_lvm_zostera}
write_rds(lvm.zostera, 
          here(save.dir, "lvm_zostera.RDS"))
```

Examine the biplot obtained by fitting the LVM, as well as the 20 most "important" species.   
```{r check_biplot_lvm_zostera}
lvsplot(lvm.zostera, jitter = T, biplot = TRUE, ind.spp = 20)
```

All in all, the final result resembles the nMDS ordination very much - same stretched clusters (Poda + Otmanli, Vromos pretty much apart, Gradina +- Ropotamo). I don't see much difference with the nMDS. 
The main difference seems to be the distance between the 2 years for Poda ana Otmanli - the LVM enlarges it. Have to remember to test for year effect! 
The run time is actually not that bad for the seagrasses.
The species singled out as significant are probably somewhat different - have to check!

Redo the biplot, because this one is not very pretty. I'm not adding the species on top, first because I'm too lazy to figure out the procedure for ordering them, and second because the plot gets too busy.   
```{r extract_lvm_coord_zostera}
## extract the LV coordinates of the stations from the model, so that the plot can be redone in ggplot 
lvs.coord.zostera <- as_tibble(lvm.zostera$lv.median)

## add the stations from the original zoobenthic table (order was not modified)
(lvs.coord.zostera <- lvs.coord.zostera %>% 
  bind_cols(zoo.abnd.zostera %>% select(station))
)

```

Make the plot and save it.  
```{r plot_lvm_zostera}
(plot.lvm.zostera <- ggplot(lvs.coord.zostera) + 
    geom_point(aes(x = lv1, y = lv2, colour = station)) + 
    scale_color_brewer(palette = "Set2", name = "station", 
                       labels = paste0("Z", as.numeric((unique(lvs.coord.zostera %>% pull(station)))))) +
   labs(x = "LV1", y = "LV2")
)

```

Well, this is a weird one - this plot is flipped around 0 compared to the one that boral's plotting function gives. Otherwise nothing changes - the spatial relationships between samples are preserved. I suppose it doesn't matter much - the axes are arbitrary after all, but strange that it happens.  

```{r save_plot_lvm_zostera}
## save the LVM plot for the seagrass
ggsave(file = here(figures.dir, "lvm_zostera.png"), 
       plot.lvm.zostera, 
       width = 15, units = "cm", dpi = 300)
```

##### **GLM fitting for abundance - environmental data**  
Fit GLMs to the sites x species matrix to try and explain the observed differences in community structure by the variation of the environmental parameters.  
These functions all come from package **mvabund**.  
Import the environmental data - the one cleaned, prepared and saved in the previous notebook (classical multivariate methods). It contains long-term averages for the water column data (as long-term as available, at least) at each station, repeated for each replicate, the sediment data (2013-2014), and the seagrass data (2013-2014), again repeated to the same number of replicates. Only the variables determined to be significant by PCA are kept.       
```{r import_env_data_zostera} 
env.zostera <- read_csv(here(save.dir, "env_data_ordinations_zostera.csv"))

## convert station to factor
(env.zostera <- env.zostera %>% 
    mutate(station = factor(station,
                            levels = c("Poda", "Otmanli", "Vromos", "Gradina", "Ropotamo")))
)
```
Station is a factor, the rest of the variables are numeric.  

Turn the zoobenthic data (minus the all-0 taxa) into a matrix - easier for the mvabund package and methods to deal with.  
```{r matrix_abnd_zostera}
## there is already one subset of filtered count data (32 x 94) - use it 
zoo.mvabnd.zostera <- mvabund(zoo.abnd.flt.zostera)
```

###### **manyGLM by LVM clusters**
First, let's see if the groups from the latent variable model (more or less equal to the clusters from the classical ordination) are valid, and which species exhibit a response.  
I'm going to try something new here - 1) loose clusters from the LVM ordination, 1 = Poda-Otmanli, 2 = Vromos, 3 = Gradina-Ropotamo. 2) stations as clusters, as I did before for the seagrass data, although I don't believe it's valid/justified to do so... 3) another configuration of clusters from the LVM ordination: 1 = Z1-Z2, 2 = Z3, 3 = Z4, 4 = Z5.   
```{r clusters_lvm_zostera}
## construct the vectors of the clusters by hand - first, situation 1 above
lvm.clusters.zostera.1 <- rep(1:3, times = c(16, 4, 12))
(lvm.clusters.zostera.1 <- factor(lvm.clusters.zostera.1))

## again, for case 2
lvm.clusters.zostera.2 <- rep(1:5, times = c(8, 8, 4, 8, 4))
(lvm.clusters.zostera.2 <- factor(lvm.clusters.zostera.2))

## again, for case 3
lvm.clusters.zostera.3 <- rep(1:4, times = c(16, 4, 8, 4))
(lvm.clusters.zostera.3 <- factor(lvm.clusters.zostera.3))
```

**LVM clusters - case 1**
Check the model assumptions. 
1. Mean-variance assumption => determines the choice of family parameter. Can be checked by plotting residuals vs fits: if little pattern - the chosen mean-variance assumption is plausible.  
Another way: direct plotting (variance ~ mean), for each species within each factor
level.  
```{r check_mean_variance_lvm_zostera_1}
plot(manyglm(zoo.mvabnd.zostera ~ lvm.clusters.zostera.1, family = "negative.binomial"))

meanvar.plot(zoo.mvabnd.zostera ~ lvm.clusters.zostera.1, table = TRUE)
```

It's not perfect, but it's not too terrible either. 

2. Assumed relationship between mean abundance and environmental variables - link function and formula.
When quantitative variables are included in the model (for now, not relevant - will be in the next model) -> if there is a trend in size of residuals at different fitted values (e.g. U-shape,..) = violation of the log-linearity assumption.
  
Everything looks more or less fine; fit the model. 
```{r fit_glms_lvm_zostera_1}
glms.lvm.zostera.1 <- manyglm(zoo.mvabnd.zostera ~ lvm.clusters.zostera.1, 
                              family = "negative.binomial")

```

Explore the fit (residuals, diagnostic plots, etc.).  
```{r explore_glms_lvm_zostera_1}
## residuals vs fitted values
plot(glms.lvm.zostera.1)

## all traditional (g)lm diagnostic plots
plot.manyglm(glms.lvm.zostera.1, which = 1:3)

# ### source mvabund GLM plotting functions modified to use a grey palette - I just can't redo these plots on my own, the function is doing too complicated things internally to scale the x and y axes
# source(here(functions.dir, "default.plot.manyglm_grey.R"))
# source(here(functions.dir, "plot.manyglm_grey.R"))
# 
# par(mfrow = c(2,2))
# lapply(1:3, function(i) plot.manyglm.grey(glms.lvm.zostera, which = i, sub.caption = ""))
# par(mfrow = c(1, 1))

```

I really don't like the rainbow palette, but I would like to include these plots in my thesis results.. Will have to do something about it, just not right now.  
Save the model!  
```{r save_glms_lvm_zostera_1}
write_rds(glms.lvm.zostera.1, 
          here(save.dir, "glms_lvm_zostera_1.RDS"))
```


Let's see the model summary (NB takes a LOT of time if there are many resamplings!).  
```{r summary_glms_lvm_zostera_1}
(glms.lvm.zostera.1.summary <- summary(glms.lvm.zostera.1, 
                                  test = "LR", p.uni = "adjusted",
                                  nBoot = 999, ## limit the number of permutations if you just want to check it out
                                  show.time = "all")
)
```

The factor is highly significant according to the models.  
This also allows us to see which species exhibit a response to the chosen factor. 
The LR (likelihood ratio) statistic is used as a measure of the strength of individual taxon contributions to the observed patterns. 
I'll save the summary for safekeeping, but I'll also run an anova - to get an analysis of deviance table on the model fit (also better for extracting the species contributions, or at least I know how to do it).  
```{r save_summary_glms_lvm_zostera_1}
write_rds(glms.lvm.zostera.1.summary, 
          here(save.dir, "glms_lvm_zostera_1_summary.RDS"))
```

Run the anova on the model. 
```{r anova_glms_lvm_zostera_1}
(glms.lvm.zostera.1.aov <- anova.manyglm(glms.lvm.zostera.1, 
                                    test = "LR", p.uni = "adjusted", 
                                    nBoot = 999, ## limit the number of permutations for a shorter run time   
                                    show.time = "all") 
)
```

Save the ANOVA, too.  
```{r save_anova_glms_lvm_zostera_1}
write_rds(glms.lvm.zostera.1.aov, 
          here(save.dir, "glms_lvm_zostera_1_anova.RDS"))
```

NOW let's get the taxa with the highest contributions to the tested pattern.  
```{r relative_taxon_contrib_glms_lvm_zostera_1}
## get the top contributing species for the initial zostera GLMs 
(top.sp.glms.lvm.zostera.1 <- top_n_sp_glm(glms.lvm.zostera.1.aov, tot.dev.expl = 0.75)
)

## unfortunately, mvabund likes to rename my species when converting the data to matrix (no spaces in names), and since I'm going to look them up in my initial untransformed count data, I have to change them back..   
names(top.sp.glms.lvm.zostera.1) <- names(top.sp.glms.lvm.zostera.1) %>% 
  str_replace(pattern = "\\.", replacement = " ")

top.sp.glms.lvm.zostera.1
```

Try to plot these top contributing species - for whatever that's worth, because 50 species on a plot is still a monstrosity.  

```{r plot_relative_taxon_contrib_glms_lvm_zostera_1}
## get the species and their abundances from the original count data, and transform them to long format
(abnd.top.sp.glms.lvm.zostera.1 <- zoo.abnd.zostera %>% 
   select(station, names(top.sp.glms.lvm.zostera.1)) %>% 
   gather(key = "species", value = "count", -station) %>% 
   ## turn species into a factor, or you'll be very very sorry later, when they're out of order on the plot. NB need to be in REVERSE order, because ggplot plots from bottom to top, and I want the top-contributing species on top. 
   mutate(species = factor(species, levels = rev(names(top.sp.glms.lvm.zostera.1))))
)


(plot.top.sp.glms.lvm.zostera.1 <- plot_top_n(abnd.top.sp.glms.lvm.zostera.1,
                                         mapping = aes(x = species, y = log_y_min(count), colour = station),
                                         labs.legend = paste0("Z", as.numeric(unique(abnd.top.sp.glms.lvm.zostera.1$station))),
                                         lab.y = "Abundance (log(y/min + 1))",
                                         palette = "Set2"
                                        ) +
    theme(legend.position = "top")

)
```

Well this is a nightmarish plot, but more tolerable than the sand one - there are less species here, so at least it's readable..   

Extract the top-contributing species to each cluster (this same nightmare above, but as a table). This chunk is STILL hopelessly ugly and clumsy.  
```{r table_relative_taxon_contrib_glms_lvm_zostera_1}
top.sp.abnd.glms.lvm.zostera.1 <- lapply(names(glms.lvm.zostera.1.summary$aliased), function(x) top_sp_glms_table(glms.lvm.zostera.1.summary, x, p = 0.05)) 

## fix species names (remove dot) 
top.sp.abnd.glms.lvm.zostera.1 <- lapply(top.sp.abnd.glms.lvm.zostera.1, function(x) x %>% mutate(species = str_replace(species, pattern = "\\.", replacement = " ")))

## rename columns (= group names) - right now they are something like "lvm.clusters.zostera2" etc.
top.sp.abnd.glms.lvm.zostera.1 <- lapply(top.sp.abnd.glms.lvm.zostera.1, function(x) x %>% rename_at(vars(contains("lvm.clusters.zostera.1")), list(~str_replace_all(., pattern = "lvm.clusters.zostera.1", "group_"))))

top.sp.abnd.glms.lvm.zostera.1 <- lapply(top.sp.abnd.glms.lvm.zostera.1, function(x) x %>% rename_at(vars(contains("Intercept")), list(~str_replace_all(., pattern = "\\(Intercept\\)", "group_1"))))


## pull the abundances from the original count df and add to the summary glm tables 
## make a long df of abundances & add clusters  
zoo.abnd.zostera.long.1 <- zoo.abnd.zostera %>%
  select(-c(month:replicate)) %>%
  gather(key = "species", value = "count", -station) %>% 
  mutate(group = case_when(station %in% c("Poda", "Otmanli") ~ 1, 
                           station == "Vromos" ~ 2, 
                           station %in% c("Gradina", "Ropotamo") ~ 3)
         )

## sum sp abundances by group; nest by group
zoo.abnd.zostera.long.1.smry <- zoo.abnd.zostera.long.1 %>% 
  group_by(species, group) %>% 
  summarise(total_count = sum(count)) %>% 
  group_by(group) %>%
  nest()

## add the counts to the group dfs - wow that's an ugly, ugly hack. Wish I had more time to write this up properly.. 
top.sp.abnd.glms.lvm.zostera.1 <- map2(top.sp.abnd.glms.lvm.zostera.1, zoo.abnd.zostera.long.1.smry %>% pull(group), ~left_join(.x, zoo.abnd.zostera.long.1.smry %>% filter(group == .y) %>% unnest(), by = "species"))

## since these are sum counts over all the replicates (that's why the monstrous numbers), average them to be mean counts per group. NB different groups consist of different numbers of replicates, b.c. some groups consist of more than one station
(top.sp.abnd.glms.lvm.zostera.1 <- map2(top.sp.abnd.glms.lvm.zostera.1, c(16, 4, 12), function(x, y) x %>% mutate(mean_count = total_count/y))
)
```

In this case, the model shows which species exhibit a reaction based on the chosen groups - in other words, which species are more likely to be more/less abundant in each group.  
I have to say, in the case of the seagrasses and case 1 clusters, there are much fewer species that exhibit a significant response - around 10 for each group.     
The LRs are lower for groups 2 and 3 - not sure if this means anything, but for group 1 they are much much higher..   
For **group 1** (= Z1-Z2), the species/taxa with significantly **higher abundance** are: Bittium reticulatum, Capitella minima, Oligochaeta, H. filiformis, Polydora ciliata, Prionospio cirrifera, R. membranacea, A. alba, A.diadema, M. acherusicum; and the only one with a significantly **lower abundance** - Chamelea gallina.   
For **group 2** (= Z3), the species with **higher abundance** are: M. acherusicum, S. filicornis, A.dadema. The species with **lower abundance** are: B. reticulatum, A. alba, Oligochaeta, S. clavata, P. ciliata, P. cirrifera, H. filiformis.  
For **group 3** (= Z4-Z5), the species with **higher abundance** are: Cumella limicola, Apseudopsis ostroumovi, Capitella capitata, Mytilaster lineatus, Loripes orbiculatus; less so, but still present - C. gallina, S. clavata. The species with **lower abundance** are: Abra alba, Melinna palmata (totally absent).  


I'll test each station as its own group, too (as I did before, with the classical multivariate methods) - I'm not sure how much I can trust this grouping (in particular group 3 is a bit far-fetched, if you ask me..).  


**LVM clusters - case 2**
Check the model assumptions.  
```{r check_mean_variance_lvm_zostera_2}
plot(manyglm(zoo.mvabnd.zostera ~ lvm.clusters.zostera.2, family = "negative.binomial"))

meanvar.plot(zoo.mvabnd.zostera ~ lvm.clusters.zostera.2, table = TRUE)
```

It's not perfect, but it's not too terrible either. I think it's a little worse than the case 1 fit.  

2. Assumed relationship between mean abundance and environmental variables - link function and formula.

Everything looks more or less fine; fit the model. 
```{r fit_glms_lvm_zostera_2}
glms.lvm.zostera.2 <- manyglm(zoo.mvabnd.zostera ~ lvm.clusters.zostera.2, 
                              family = "negative.binomial")

```

Explore the fit (residuals, diagnostic plots, etc.).  
```{r explore_glms_lvm_zostera_2}
## residuals vs fitted values
plot(glms.lvm.zostera.2)

## all traditional (g)lm diagnostic plots
plot.manyglm(glms.lvm.zostera.2, which = 1:3)

# ### source mvabund GLM plotting functions modified to use a grey palette - I just can't redo these plots on my own, the function is doing too complicated things internally to scale the x and y axes
# source(here(functions.dir, "default.plot.manyglm_grey.R"))
# source(here(functions.dir, "plot.manyglm_grey.R"))
# 
# par(mfrow = c(2,2))
# lapply(2:3, function(i) plot.manyglm.grey(glms.lvm.zostera, which = i, sub.caption = ""))
# par(mfrow = c(2, 2))

```

Save the model!  
```{r save_glms_lvm_zostera_2}
write_rds(glms.lvm.zostera.2, 
          here(save.dir, "glms_lvm_zostera_2.RDS"))
```


Let's see the model summary (NB takes a LOT of time if there are many resamplings!).  
```{r summary_glms_lvm_zostera_2}
(glms.lvm.zostera.2.summary <- summary(glms.lvm.zostera.2, 
                                       test = "LR", p.uni = "adjusted",
                                       nBoot = 999, ## limit the number of permutations if you just want to check it out
                                       show.time = "all")
)
```

The factor is highly significant according to the models.  
 
Again, save the summary for safekeeping, but also run an anova.  
```{r save_summary_glms_lvm_zostera_2}
write_rds(glms.lvm.zostera.2.summary, 
          here(save.dir, "glms_lvm_zostera_2_summary.RDS"))
```

Run the anova on the model. 
```{r anova_glms_lvm_zostera_2}
(glms.lvm.zostera.2.aov <- anova.manyglm(glms.lvm.zostera.2, 
                                         test = "LR", p.uni = "adjusted", 
                                         nBoot = 999, ## limit the number of permutations for a shorter run time   
                                         show.time = "all") 
)
```

Save the ANOVA, too.  
```{r save_anova_glms_lvm_zostera_2}
write_rds(glms.lvm.zostera.2.aov, 
          here(save.dir, "glms_lvm_zostera_2_anova.RDS"))
```

NOW let's get the taxa with the highest contributions to the tested pattern.  
```{r relative_taxon_contrib_glms_lvm_zostera_2}
## get the top contributing species for the initial zostera GLMs 
(top.sp.glms.lvm.zostera.2 <- top_n_sp_glm(glms.lvm.zostera.2.aov, tot.dev.expl = 0.75)
)

## unfortunately, mvabund likes to rename my species when converting the data to matrix (no spaces in names), and since I'm going to look them up in my initial untransformed count data, I have to change them back..   
names(top.sp.glms.lvm.zostera.2) <- names(top.sp.glms.lvm.zostera.2) %>% 
  str_replace(pattern = "\\.", replacement = " ")

top.sp.glms.lvm.zostera.2
```

Try to plot these top contributing species - for whatever that's worth, because 50 species on a plot is still a monstrosity.  

```{r plot_relative_taxon_contrib_glms_lvm_zostera_2}
## get the species and their abundances from the original count data, and transform them to long format
(abnd.top.sp.glms.lvm.zostera.2 <- zoo.abnd.zostera %>% 
   select(station, names(top.sp.glms.lvm.zostera.2)) %>% 
   gather(key = "species", value = "count", -station) %>% 
   ## turn species into a factor, or you'll be very very sorry later, when they're out of order on the plot. NB need to be in REVERSE order, because ggplot plots from bottom to top, and I want the top-contributing species on top. 
   mutate(species = factor(species, levels = rev(names(top.sp.glms.lvm.zostera.2))))
)


(plot.top.sp.glms.lvm.zostera.2 <- plot_top_n(abnd.top.sp.glms.lvm.zostera.2,
                                              mapping = aes(x = species, y = log_y_min(count), colour = station),
                                              labs.legend = paste0("Z", as.numeric(unique(abnd.top.sp.glms.lvm.zostera.2$station))),
                                              lab.y = "Abundance (log(y/min + 1))",
                                              palette = "Set2"
                                        ) +
    theme(legend.position = "top")

)
```


Extract the top-contributing species to each cluster (this same nightmare above, but as a table). This chunk is STILL hopelessly ugly and clumsy.  
```{r table_relative_taxon_contrib_glms_lvm_zostera_2}
top.sp.abnd.glms.lvm.zostera.2 <- lapply(names(glms.lvm.zostera.2.summary$aliased), function(x) top_sp_glms_table(glms.lvm.zostera.2.summary, x, p = 0.05)) 

## fix species names (remove dot) 
top.sp.abnd.glms.lvm.zostera.2 <- lapply(top.sp.abnd.glms.lvm.zostera.2, function(x) x %>% mutate(species = str_replace(species, pattern = "\\.", replacement = " ")))

## rename columns (= group names) - right now they are something like "lvm.clusters.zostera2" etc.
top.sp.abnd.glms.lvm.zostera.2 <- lapply(top.sp.abnd.glms.lvm.zostera.2, function(x) x %>% rename_at(vars(contains("lvm.clusters.zostera.2")), list(~str_replace_all(., pattern = "lvm.clusters.zostera.2", "group_"))))

top.sp.abnd.glms.lvm.zostera.2 <- lapply(top.sp.abnd.glms.lvm.zostera.2, function(x) x %>% rename_at(vars(contains("Intercept")), list(~str_replace_all(., pattern = "\\(Intercept\\)", "group_1"))))


## pull the abundances from the original count df and add to the summary glm tables 
## make a long df of abundances & add clusters  
zoo.abnd.zostera.long.2 <- zoo.abnd.zostera %>%
  select(-c(month:replicate)) %>%
  gather(key = "species", value = "count", -station) %>% 
  mutate(group = case_when(station == "Poda" ~ 1,
                           station == "Otmanli" ~ 2, 
                           station == "Vromos" ~ 3, 
                           station == "Gradina" ~ 4, 
                           station == "Ropotamo" ~ 5)
         )

## sum sp abundances by group; nest by group
zoo.abnd.zostera.long.2.smry <- zoo.abnd.zostera.long.2 %>% 
  group_by(species, group) %>% 
  summarise(total_count = sum(count)) %>% 
  group_by(group) %>%
  nest()

## add the counts to the group dfs - wow that's an ugly, ugly hack. Wish I had more time to write this up properly.. 
top.sp.abnd.glms.lvm.zostera.2 <- map2(top.sp.abnd.glms.lvm.zostera.2, zoo.abnd.zostera.long.2.smry %>% pull(group), ~left_join(.x, zoo.abnd.zostera.long.2.smry %>% filter(group == .y) %>% unnest(), by = "species"))

## since these are sum counts over all the replicates (that's why the monstrous numbers), average them to be mean counts per group. NB different groups consist of different numbers of replicates, b.c. some groups consist of more than one station
(top.sp.abnd.glms.lvm.zostera.2 <- map2(top.sp.abnd.glms.lvm.zostera.2, c(8, 8, 4, 8, 4), function(x, y) x %>% mutate(mean_count = total_count/y))
)
```

In the case of the seagrasses and case 2 clusters (= stations), the picture is still more unclear.. I suppose this is in no small part because of the differences 2013-14 - very marked for Poda and Otmanli. I suspect the stations changed in these two years (we were looking for Z. noltii in 2014 in particular) - but still, there is much variability. In the future, it's probably going to be worth it to have more stations in a meadow, if we really want to have an idea of the communities there, and their variability.  
The LRs seem to be a bit lower for groups 2, 4, maybe 5 too - still not sure if you can use that as a significance measure.  
For now, in **group 1** (= Z1), it's hard to pick some characteristic species - because of the variability between 2013-2014, no doubt. The species/taxa with significantly **higher abundance** are: Bittium reticulatum, Capitella minima, Polydora ciliata, Prionosprio cirrifera (+ others, medium abundance); and the ones with a significantly **lower abundance** - or even absent - C. gallina, A. ostroumovi, S. clavata, C. limicola, C. costulata, S. hystrix, S. gracilis, T. pullus.   
For **group 2** (= Z2), the species with **higher abundance** - which is not really all that high; this group is also loose, hard to distinguish from group 1 - are: S. gracilis, M. lineatus, P. ciliata. The only species with **lower abundance** - in fact 0 - is Alitta succinea.  
For **group 3** (= Z3), the species with **higher abundance** are: M. acherusicum, S. filicornis, A. diadema. The species with **lower abundance** (or 0) are: B. reticulatum, P. ciliata, P. cirrifera, A. alba, A. succiena, S. clavata, Oligochaeta, A. improvisus.  
For **group 4** (= Z4), the species with **higher abundance** are: M. lineatus (very much so); C. limicola, P. kefersteini, C. gallina, C. capitata. The species with **lower abundance** (or 0) are: P. ciliata, P. cirrifera, A. succinea, A. improvisus, A. alba.  
For **group 5** (= Z5), the species with **higher abundance** are: A. ostroumovi, C. capitata, Oligochaeta. The species with **lower abundance** (or 0) are: R. splendida, T. pullus.  


**LVM clusters - case 3**
Last try: group 1 = Z1-Z2, group 2 = Z3, group 3 = Z4, group 4 = Z5.  
Check the model assumptions.  
```{r check_mean_variance_lvm_zostera_3}
plot(manyglm(zoo.mvabnd.zostera ~ lvm.clusters.zostera.3, family = "negative.binomial"))

meanvar.plot(zoo.mvabnd.zostera ~ lvm.clusters.zostera.3, table = TRUE)
```

More or less the same as case 2 before it. 

2. Assumed relationship between mean abundance and environmental variables - link function and formula.

Everything looks more or less fine; fit the model. 
```{r fit_glms_lvm_zostera_3}
glms.lvm.zostera.3 <- manyglm(zoo.mvabnd.zostera ~ lvm.clusters.zostera.3, 
                              family = "negative.binomial")

```

Explore the fit (residuals, diagnostic plots, etc.).  
```{r explore_glms_lvm_zostera_3}
## residuals vs fitted values
plot(glms.lvm.zostera.3)

## all traditional (g)lm diagnostic plots
plot.manyglm(glms.lvm.zostera.3, which = 1:3)

# ### source mvabund GLM plotting functions modified to use a grey palette - I just can't redo these plots on my own, the function is doing too complicated things internally to scale the x and y axes
# source(here(functions.dir, "default.plot.manyglm_grey.R"))
# source(here(functions.dir, "plot.manyglm_grey.R"))
# 
# par(mfrow = c(3,3))
# lapply(3:3, function(i) plot.manyglm.grey(glms.lvm.zostera, which = i, sub.caption = ""))
# par(mfrow = c(3, 3))

```

Save the model!  
```{r save_glms_lvm_zostera_3}
write_rds(glms.lvm.zostera.3, 
          here(save.dir, "glms_lvm_zostera_3.RDS"))
```


Let's see the model summary (NB takes a LOT of time if there are many resamplings!).  
```{r summary_glms_lvm_zostera_3}
(glms.lvm.zostera.3.summary <- summary(glms.lvm.zostera.3, 
                                       test = "LR", p.uni = "adjusted",
                                       nBoot = 999, ## limit the number of permutations if you just want to check it out
                                       show.time = "all")
)
```

The factor is highly significant according to the models.  
 
Again, save the summary for safekeeping, but also run an anova.  
```{r save_summary_glms_lvm_zostera_3}
write_rds(glms.lvm.zostera.3.summary, 
          here(save.dir, "glms_lvm_zostera_3_summary.RDS"))
```

Run the anova on the model. 
```{r anova_glms_lvm_zostera_3}
(glms.lvm.zostera.3.aov <- anova.manyglm(glms.lvm.zostera.3, 
                                         test = "LR", p.uni = "adjusted", 
                                         nBoot = 999, ## limit the number of permutations for a shorter run time   
                                         show.time = "all") 
)
```

Save the ANOVA, too.  
```{r save_anova_glms_lvm_zostera_3}
write_rds(glms.lvm.zostera.3.aov, 
          here(save.dir, "glms_lvm_zostera_3_anova.RDS"))
```

NOW let's get the taxa with the highest contributions to the tested pattern.  
```{r relative_taxon_contrib_glms_lvm_zostera_3}
## get the top contributing species for the initial zostera GLMs 
(top.sp.glms.lvm.zostera.3 <- top_n_sp_glm(glms.lvm.zostera.3.aov, tot.dev.expl = 0.75)
)

## unfortunately, mvabund likes to rename my species when converting the data to matrix (no spaces in names), and since I'm going to look them up in my initial untransformed count data, I have to change them back..   
names(top.sp.glms.lvm.zostera.3) <- names(top.sp.glms.lvm.zostera.3) %>% 
  str_replace(pattern = "\\.", replacement = " ")

top.sp.glms.lvm.zostera.3
```

Try to plot these top contributing species - for whatever that's worth, because 50 species on a plot is still a monstrosity.  

```{r plot_relative_taxon_contrib_glms_lvm_zostera_3}
## get the species and their abundances from the original count data, and transform them to long format
(abnd.top.sp.glms.lvm.zostera.3 <- zoo.abnd.zostera %>% 
   select(station, names(top.sp.glms.lvm.zostera.3)) %>% 
   gather(key = "species", value = "count", -station) %>% 
   ## turn species into a factor, or you'll be very very sorry later, when they're out of order on the plot. NB need to be in REVERSE order, because ggplot plots from bottom to top, and I want the top-contributing species on top. 
   mutate(species = factor(species, levels = rev(names(top.sp.glms.lvm.zostera.3))))
)


(plot.top.sp.glms.lvm.zostera.3 <- plot_top_n(abnd.top.sp.glms.lvm.zostera.3,
                                              mapping = aes(x = species, y = log_y_min(count), colour = station),
                                              labs.legend = paste0("Z", as.numeric(unique(abnd.top.sp.glms.lvm.zostera.3$station))),
                                              lab.y = "Abundance (log(y/min + 1))",
                                              palette = "Set2"
                                        ) +
    theme(legend.position = "top")

)
```


Extract the top-contributing species to each cluster (this same nightmare above, but as a table). This chunk is STILL hopelessly ugly and clumsy.  
```{r table_relative_taxon_contrib_glms_lvm_zostera_3}
top.sp.abnd.glms.lvm.zostera.3 <- lapply(names(glms.lvm.zostera.3.summary$aliased), function(x) top_sp_glms_table(glms.lvm.zostera.3.summary, x, p = 0.05)) 

## fix species names (remove dot) 
top.sp.abnd.glms.lvm.zostera.3 <- lapply(top.sp.abnd.glms.lvm.zostera.3, function(x) x %>% mutate(species = str_replace(species, pattern = "\\.", replacement = " ")))

## rename columns (= group names) - right now they are something like "lvm.clusters.zostera3" etc.
top.sp.abnd.glms.lvm.zostera.3 <- lapply(top.sp.abnd.glms.lvm.zostera.3, function(x) x %>% rename_at(vars(contains("lvm.clusters.zostera.3")), list(~str_replace_all(., pattern = "lvm.clusters.zostera.3", "group_"))))

top.sp.abnd.glms.lvm.zostera.3 <- lapply(top.sp.abnd.glms.lvm.zostera.3, function(x) x %>% rename_at(vars(contains("Intercept")), list(~str_replace_all(., pattern = "\\(Intercept\\)", "group_1"))))


## pull the abundances from the original count df and add to the summary glm tables 
## make a long df of abundances & add clusters  
zoo.abnd.zostera.long.3 <- zoo.abnd.zostera %>%
  select(-c(month:replicate)) %>%
  gather(key = "species", value = "count", -station) %>% 
  mutate(group = case_when(station %in% c("Poda", "Otmanli") ~ 1,
                           station == "Vromos" ~ 2, 
                           station == "Gradina" ~ 3, 
                           station == "Ropotamo" ~ 4)
         )

## sum sp abundances by group; nest by group
zoo.abnd.zostera.long.3.smry <- zoo.abnd.zostera.long.3 %>% 
  group_by(species, group) %>% 
  summarise(total_count = sum(count)) %>% 
  group_by(group) %>%
  nest()

## add the counts to the group dfs - wow that's an ugly, ugly hack. Wish I had more time to write this up properly.. 
top.sp.abnd.glms.lvm.zostera.3 <- map2(top.sp.abnd.glms.lvm.zostera.3, zoo.abnd.zostera.long.3.smry %>% pull(group), ~left_join(.x, zoo.abnd.zostera.long.3.smry %>% filter(group == .y) %>% unnest(), by = "species"))

## since these are sum counts over all the replicates (that's why the monstrous numbers), average them to be mean counts per group. NB different groups consist of different numbers of replicates, b.c. some groups consist of more than one station
(top.sp.abnd.glms.lvm.zostera.3 <- map2(top.sp.abnd.glms.lvm.zostera.3, c(16, 4, 8, 4), function(x, y) x %>% mutate(mean_count = total_count/y))
)
```

In the case of the seagrasses and case 3 clusters, the picture is still more confusing..  
The LRs seem to be a bit lower for groups 2 and 3, maybe 4 too - still not sure if you can use that as a significance measure.  
For now, in **group 1** (= Z1-Z2), the species/taxa with significantly **higher abundance** are: Bittium reticulatum, Capitella minima, Oligochaeta, Heteromastus filiformis, Polydora ciliata, Prionosprio cirrifera, Rissoa membranacea, Abra alba, Ampelisca diadema (+ others, medium abundance); and the ones with a significantly **lower abundance** - or even absent -  S. clavata,  A. ostroumovi, C. gallina, T. pullus.   
There are more species singled out for this cluster, probably because of the variability between the two years of sampling.  
For **group 2** (= Z3), the species with **higher abundance** are: M. acherusicum, S. filicornis, A. diadema. The species with **lower abundance** - in fact 0 - are B. reticulatum, P. cirrifera, S. clavata, A. alba, P. ciliata, oligochaetes, H. filiformis, R. splendida.  
For **group 3** (= Z4), the species with **higher abundance** are: M. lineatus, less so - C. limicola, L. orbiculatus, P. kefersteini, C. capitata, etc. The species with **lower abundance** (or 0) are: P. cirrifera, P. ciliata, A. alba, etc.  
For **group 4** (= Z5), the species with **higher abundance** are: A. ostoumovi, C. capitata, oligochaetes (very abundant, but with a small LR - nice!). The species with **lower abundance** (or 0) are: R. splendida, S. clavata, C. limicola.  


**All in all, I think that group 1 (Poda + Otmanli) holds, and so does group 2 (Vromos). The question is whether it makes sense to separate Gradina and Ropotamo into 2 groups, or if they make more sense together. Ropotamo is characterized by a very high number of oligochaetes, while Gradina's most distinguishing characteristic is the high number of M. lineatus - mostly very small ones, attached to the rhizomes, close to the sediment surface I presume. Both stations have C. limicola in medium abundance, which is not present anywhere else.** 


Try to compare the three models.. 
```{r compare_glms_lvm_zostera}
(glms.lvm.zostera.comp <- anova(glms.lvm.zostera.1,
                                glms.lvm.zostera.2, 
                                glms.lvm.zostera.3, 
                                p.uni = "adjusted")
)

```

Well I don't know how to interpret that.. Have to check the manual first. 